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The experimental two-microphone transfer function method (TMTF) is adapted to the numerical framework to compute the radiation and input impedances of three-dimensional vocal tracts of elliptical cross section. In its simplest version, the TMTF method only requires measuring the acoustic pressure at two points in an impedance duct and the postprocessing of the corresponding transfer function. However, some considerations are to be taken into account when using the TMTF method in the numerical context, which constitute the main objective of this paper. In particular, the importance of including absorption at the impedance duct walls to avoid lengthy numerical simulations is discussed and analytical complex axial wave numbers for elliptical ducts are derived for this purpose. It is also shown how the plane wave restriction of the TMTF method can be circumvented to some extent by appropriate location of the virtual microphones, thus extending the method frequency range of validity. Virtual microphone spacing is also discussed on the basis of the so called singularity factor. Numerical examples include the computation of the radiation impedance of vowels /a/, /i/ and /u/ and the input impedance of vowel /a/, for simplified vocal tracts of circular and elliptical cross sections.

The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some portions of the computational domain, e.g., near the domain boundary or near long narrow channels inside the domain due to the lack of permeability information outside of the domain or the fact that the high-conductivity features cannot be localized within a coarse-grid block. In this paper we develop a combined finite element and multiscale finite element method (FE-MsFEM), which deals with such portions by using the standard finite element method on a fine mesh and the other portions by the oversampling MsFEM. The transmission conditions across the FE-MSFE interface is treated by the penalty technique. A rigorous convergence analysis for this special FE-MsFEM is given under the assumption that the diffusion coefficient is periodic. Numerical experiments are carried out for the elliptic equations with periodic and random highly oscillating coefficients, as well as multiscale problems with high contrast channels, to demonstrate the accuracy and efficiency of the proposed method.

A challenging difficulty in solving the radial Dirac eigenvalue problem numerically is the presence of spurious (unphysical) eigenvalues among the correct ones that are neither related to mathematical interpretations nor to physical explanations. Many attempts have been made and several numerical methods have been applied to solve the problem using finite element method (FEM), finite difference method (FDM), or other numerical schemes. Unfortunately most of these attempts failed to overcome the difficulty. As a FEM approach, this work can be regarded as a first promising scheme to solve the spuriousity problem completely. Our approach is based on an appropriate choice of trial and test functional spaces. We develop a Streamline Upwind Petrov-Galerkin method (SUPG) to the equation and derive an explicit stability parameter.

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An optimal order error estimate is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknown variables on each element, yielding a significantly reduced system of linear equations for unknowns on the boundary of each element.

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An optimal order error estimate is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknown variables on each element, yielding a significantly reduced system of linear equations for unknowns on the boundary of each element.

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An optimal order error estimate is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknown variables on each element, yielding a significantly reduced system of linear equations for unknowns on the boundary of each element.

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier is verified to provide a numerical approximation for certain derivatives of the exact solution. An optimal order error estimate is established for the numerical approximations arising from the hybridized weak Galerkin finite element method. The paper also derives a computational algorithm (Schur complement) by eliminating all the unknown variables on each element, yielding a significantly reduced system of linear equations for unknowns on the boundary of each element.

This article is from Journal of the Royal Society Interface , volume 11 . Abstract Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.

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This paper studies the nonconforming Morley finite element approximation of the eigenvalues of the biharmonic operator. A new $C^1$ conforming companion operator leads to an $L^2$ error estimate for the Morley finite element method which directly compares the $L^2$ error with the error in the energy norm and, hence, can dispense with any additional regularity assumptions. Furthermore, the paper presents new eigenvalue error estimates for nonconforming finite elements that bound the error of (possibly multiple or clustered) eigenvalues by the approximation error of the computed invariant subspace. An application is the proof of optimal convergence rates for the adaptive Morley finite element method for eigenvalue clusters.

The finite element method was used to solve the nonlinear, small-disturbance, transonic, velocity-potential equation for problems of steady flow over a circular cylinder and over a thin-airfoil in a uniform steady airstream. The governing differential equation is valid for inviscid, irrotational, isenthropic flow of a perfect gas to include weak shocks providing airflow separation does not occur. For compressible subsonic and transonic flows the nonlinear small-disturbance equation was expressed in iterative form as a sequence of linear equations which was solved iteratively until the difference between two successive solutions became arbitrarily small. For analysis purposes the infinite flowfield was replaced by a finite but sufficiently large domain that was discretized with sector elements for the cylinder problem and rectangular elements for the airfoil problem. Three sub-problems were investigated for the circular cylinder. First, three different types of trial functions were investigated to approximate the solution for the velocity potential function for the case of incompressible flow without circulation. The three trial functions were: (1) a trignometric approximation resulting in a non-conforming element, (2) a bilinear polynomial (conforming element) typical of elements used in finite element analysis, and (3) a rational approximation resulting in a new conforming element. Convergence properties of each element were studied as a function of discretization refinement (element size). The second subproblem for the cylinder was to use the two conforming elements to obtain solutions for incompressible flow with circulation. Superposition was used to split the total problem into two elementary component problems.

Discussed are some aspects of implementing the finite element method on parallel computers with local memory and message passing. In particular, the costs of using high order and low order elements, and of direct and iterative solvers are compared for solving the linear systems that occur. Our model of parallel computation is a two-dimensional grid of processors chosen to be similar in shape to the underlying grid. Our main conclusions are that sparse direct solvers generalize naturally to methods based on high order elements, and that direct solvers are adequate for two-dimensional problems, especially for multiple load vectors. High order methods are shown to achieve higher accuracy at less cost on some typical model problems.

This paper describes a finite element approach to quasi-TEM analysis of several different types of isolated and coupled microwave transmission lines. Both the first and higher-order ordinary elements, as well as singular and infinite elements are used to solve for the potential and field distribution in the cross-section of the line. Next, the cross-sectional field distribution is inserted in a variational expression to compute the capacitance per unit length of the line and the effective e permittivity and characteristic impedance of the line are obtained from the capacitance value. A perturbational approach is developed for estimating the losses due to conductor and dielectric dissipation and computing the attenuation constant. Lines treatable by this method may contain an arbitrary number of arbitrarily shaped conductors, including a system of conductors either placed above a single ground plane or between two parallel ground planes, and inhomogeneous dielectric regions that can be approximated locally by a number of homogeneous subregions. Keywords include: Microwave & millimeter waves; Digital circuits; Transmission lines; Characteristic impedance; Dielectric losses; Conductor losses; and Finite element method.

This final technical report presents a summary of a three years project in which the mathematical basis of failure criteria for metals and composite materials was investigated. The investigation covered criteria associated with crack formation and structural instability. The main results are: (a) General procedures for the determination of mathematical functions that model the conditions for crack formation at critical points were developed and implemented into a generally available computer code. (b) Mathematical models for buckling failure were formulated, implemented and their properties clarified.

The paper surveys the approximation and convergence properties of the h-p version of the finite element method, the basic theoretical results together with the main ideas of the proofs. Numerical examples are given.

This report is a part of a Corps-wide project to provide guidance for the use of finite element analyses. A continuation of the Phase Ia study dealing with a static finite element analysis of a gravity dam and Phase Ib study dealing with foundation-structure interaction, Phase II gives direction in performing a response-spectrum dynamic finite element analysis of a gravity dam. An example problem is presented to demonstrate how to verify the results for a simplified structure before moving to the analysis of the real structure. An analysis of a realistic gravity dam is then presented with results. The primary objective of this study is to give direction in performing a response-spectrum dynamic finite element analysis of a gravity dam using a general-purpose computer program. (SDW)

The finite element method may relieve some of the problems associated with numerical modelling of the atmosphere. The method reduces the problem of nonlinear computational instability, allows arbitrary placement of grid points, and offers greater flexibility in the handling of boundary conditions. In addition, the finite element method has been shown to be more accurate for some types of problems. This research concentrates on the ability of the finite element method to serve as the means of solving the equations which describe flow in the atmosphere and provides answers as to the type of finite element approximation best suited for meteorological research. Five different finite elements using both linear and quadratic interpolation are tested in the space domain. Several time differencing schemes are also tested with the elements in order to determine the most accurate and efficient configuration. In addition, the concepts of lumped and consistent mass are examined and tested as well as alternative methods of handling the computer implementation of the method.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

The use of object-oriented programming techniques in development of parallel, finite element analysis software enhances software reused and makes application development more efficient. In this report, an object-oriented programming framework for developing parallel finite element software is described. All required steps, from date file parsing and equation solving to post processing and graphical user interfaces, are discussed. After development of the framework, a sample parallel finite element code, namely COMPOSE, is extracted from its original functional programming paradigm and implemented in the new object-oriented programming framework. Besides ease of development, the use of generic visualization and interface tools for software using the framework speeds delivery of research codes to end users.

This engineer technical letter provides guidance on the use of the finite element method in the analysis of problems in geotechnical engineering. This ETL is intended for engineers who are unfamiliar with the method, but who are interested in understanding its potential use in geotechnical engineering.

In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions. In particular, we show that the superconvergence points for the gradient of the approximate are zeros of certain systems of non-linear equations that do not depend on the solution of the boundary value problem. For approximate solutions with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate solution as the roots of certain systems of non-linear equations. We note that it is easy to construct smooth generalized finite element approximation.

Two primary thrusts have been put forth in our recent work on the quasicontinuum method. First, the method was generalized so as to allow for the treatment of materials involving multiple grains. A second key development has been the extension of the method to three dimensions. These developments have made it possible to examine the detailed microscopic mechanisms that accompany defect interactions. In particular, we have examined dislocation-grain boundary interactions, crack-grain boundary interactions and dislocation-dislocation interactions.

A significant increase in pore water pressure during construction of earth dams may lead to the hydraulic fracture of dam body in pounding. Thus having sufficient information about generation pattern of excess pore water pressure inside the core is essential. In the present study, using finite element method in coupled analysis of earth dams, excess pore water pressure and displacement values are estimated during the construction of Daroongar dam by developed Fortran code, and the results were compared with instrumentation data. Finally the actual amounts of horizontal and vertical permeability coefficients were determined for the materials by regression analysis.

The search for more efficient gas turbine engines has led to the proposal for the replacement of metal high temperature components with ceramic components . Essential to this effort is the numerical analysis of proposed designs . This thesis report describes the model discretization of a proposed blade design, the development of pre- and post-processors for the ADINA finite element code and the initial stress analysis of the modeled blade.

This article is from Journal of Dentistry (Tehran, Iran) , volume 11 . Abstract Objective:: Several appliances have been used for palatal expansion for treatment of posterior cross bite. The purpose of this study was to evaluate the stress induced in the apical and crestal alveolar bone and the pattern of tooth displacement following expansion via removable expansion plates or fixed-banded palatal expander using the finite element method (FEM) analysis. Materials and Methods:: Two 3D FEM models were designed from a mesio-distal slice of the maxilla containing the upper first molars, their periodontium and alveolar bone. Two palatal expanders (removable and fixed) were modeled. The models were designed in SolidWorks 2006 and then transferred to ANSYS Workbench. The appliance halves were displaced 0.1 mm laterally. The von Mises stress in the apical, crestal, and PDL areas and also the vertical displacement of the cusps (palatal and buccal) was were evaluated. Results:: The total PDL stress was 0.40003 MPa in the removable appliance (RA) model and 4.88e-2 MPa in the fixed appliance (FA) model and the apical stress was 9.9e-2 and 1.17e-2 MPa, respectively. The crestal stress was 2.99e-1 MPa in RA and 7.62e-2 MPa in the FA. The stress in the cortical bone crest was 0.30327 and 7.9244e-2 MPa for RA and FA, respectively and 3.7271 and 7.4373e-2 MPa in crestal area of spongy bone, respectively. The vertical displacement of the buccal cusp and palatal cusp was 1.64e-2 and 5.90e-2 mm in RA and 1.05e-4 and 1.7e-4 mm in FA, respectively. Conclusion:: The overall stress as well as apical and crestal stress in periodontium of anchor teeth was higher in RA than FA; RA elicited higher stress in both cortical and spongy bone. The vertical displacement of molar cusps was more in removable than fixed palatal expander model.

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived by using standard method of operational calculus.

The survey of the basic ideas and results of the h, p and h-p versions of the finite element method is presented in this paper.

This paper describes a finite element approach to a hybrid-mode analysis of isolated and coupled microwave transmission lines. Both the first and higher-order ordinary elements, as well as singular and infinite elements, are used to solve for the eigenvalues and eigenvectors of the modes propagating along the line. Once the field distribution in the cross section of the line is known the characteristic impedance of the dominant mode propagating along the line can readily be obtained. A perturbational approach is developed for estimating the losses due to conductor and dielectric dissipation and computing the attenuation constant for each mode. Lines treatable by this method may contain an arbitrary number arbitrarily shaped conductors, including a system of conductors either placed above a single ground plane or between two parallel ground planes, and inhomogeneous dielectric regions that can be approximated locally by a number of homogeneous subregions. The results obtained using the finite element procedure have been compared for various types of microwave transmission lines and have been found to agree well with available data. (Author)

This paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting. The main emphasis is placed on the analysis when the (exact) solution has singularity of x sub alpha type. The first part analyzes the p-version, the second the h-version and general h-p version and the final third part addresses the problems of the adaptive h-p version. Additional keywords: Legendre polynomials; Legendre expansion; estimates; Asymptotic behavior; Approximation (mathematics); Analytic functions. (Author)

In this work we study the pollution-error in the h-version of the finite element method and its effect on the local quality of a-posteriori error estimators. We show that the pollution-effect in an interior subdomain depends on the relationship between the mesh inside and outside the subdomain and the smoothness of the exact solution. We also demonstrate that it is possible to guarantee the quality of local error-estimators in the interior of a finite- element mesh-patch of interest by employing meshes which axe sufficiently refined outside the patch.

Various methods for treating nonhomogeneous Dirichlet boundary conditions for the p-version of the finite element method are presented. These methods are theoretically and computationally analyzed. Numerical experimentations are given. They clearly illustrate the importance of the right treatment of the nonhomogeneous Dirichlet boundary conditions.

The complex geometry of many parts of a ceramic gas turbine engine and the need to known the stresses in these parts to a high degree of accuracy indicate that the finite element method should be employed. One analysis code used a finite element program based on an isoparametric 12-node brick. This allowed quadratic variation in one coordinate direction, but only linear variation in the other two coordinate directions. This introduced an artificial stiffness into the structure. This study was made to determine the effects of using a totally quadratic isoparametric brick, vice one which is quadratic in only one direction. A distributed load preprocessor was also developed and tested. FORTRAN IV was used throughout. (Author)

This paper is divided into three parts, First, a review of currently available incremental theories of plasticity and creep constitutive models is given. Second, a formulation is presented for the non-isothermal, elastic-plastic-creep-large strain analysis by the finite element method. Third, results obtained with the AGGIE I computer program for several isothermal, elastic-creep and elastic-plastic analyses are presented. The present numerical results show good agreement with experimental and other numerical results. (Author)

The theory of the computable a-posteriori error estimate for a finite element method is developed. Among other things, it is shown that the error estimate is very reliable and the ratio (called effectivity index) between the estimator and the true error approaches one. Numerical examples computed by program FEARS (Finite Element Adaptive Research Solver) of the University of Maryland, illustrate the effectivity and reliability of the estimators. (Author)

In the first part of this paper we study in detail the properties of the divergence operator acting on continuous piecewise polynomials; more specifically, we characterize the range and prove the existence of a maximal right-inverse whose norm grows at most algebraically with the degree of the piecewise polynomials. In the last part of this paper we apply these results to the p-version of the Finite Element Method for a nearly incompressible material with homogeneous Dirichlet boundary conditions. We show that the p-version maintains optimal convergence rates in the limit as the Poisson ratio approaches 1/2. This fact eliminates the need for any reduced integration such as customarily used in connection with the more standard h-version of the Finite Element Method. (Author)

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

A hypothesis is made that the Galerkin Finite Element Method (GFEM) offers a viable option to the traditional Finite Difference Method (FDM) for numerical weather prediction. The shallow water barotropic primitive equations are the forecast equations for all experiments. The hypothesis is tested by observing simple, analytic, atmospheric wave propagation on uniform and variable mesh grids. Second, a strongly forced solution simulating small scale nonlinear interactions is evaluated for both the GFEM and FDM. Finally, a variable, moving grid for a GFEM model is compared to a uniform, higher resolution GFEM model for a strong vortex in a mean flow. The GFEM shows a better propagation for simple atmospheric waves and better prediction to a forced nonlinear solution than the FDM model. A moving variable grid follows an area of strong gradients while not generating noise in the transition zone.

A hypothesis is made that the Galerkin Finite Element Method (GFEM) offers a viable option to the traditional Finite Difference Method (FDM) for numerical weather prediction. The shallow water barotropic primitive equations are the forecast equations for all experiments. The hypothesis is tested by observing simple, analytic, atmospheric wave propagation on uniform and variable mesh grids. Second, a strongly forced solution simulating small scale nonlinear interactions is evaluated for both the GFEM and FDM. Finally, a variable, moving grid for a GFEM model is compared to a uniform, higher resolution GFEM model for a strong vortex in a mean flow. The GFEM shows a better propagation for simple atmospheric waves and better prediction to a forced nonlinear solution than the FDM model. A moving variable grid follows an area of strong gradients while not generating noise in the transition zone.

Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a leaky waveguide with sufficient accuracy. In this paper we show that with a special goal oriented error estimator for capturing radiation losses this problem is overcome.

The primary aim of this study is to develop a finite element model for elastic scattering by axisymmetric bodies submerged in a heterogeneous ocean acoustic waveguide.

There are three versions of the finite element method. The classical h- version achieves accuracy by refining the mesh while using low degrees p of the elements, usually p = 1, 2. The p-version keeps the mesh fixed and the accuracy is achieved by increasing the degree p. The h-p version combines both approaches. Although the p and h-p versions of the finite element method are relatively new developments, many basic results are available. The aim of this paper is to give a survey of the basic available results and directions for further development. The paper tries to survey basic theoretical implementational and computational aspects of the method as of today.

The solutions of elliptic problems with a Dirac measure in right-hand side are not H1 and therefore the convergence of the finite element solutions is suboptimal. Graded meshes are standard remedy to recover quasi-optimality, namely optimality up to a log-factor, for low order finite elements in L2-norm. Optimal (or quasi-optimal for the lowest order case) convergence has been shown in L2-seminorm, where the L2-seminorm is defined as the L2-norm on a subdomain which excludes the singularity. Here we show a quasi-optimal convergence for the Hs-seminorm, s \textgreater{} 0, and an optimal convergence in H1-seminorm for the lowest order case, on a family of quasi- uniform meshes in dimension 2. This question is motivated by the use of the Dirac measure as a reduced model in physical problems, and a high accuracy at the singularity of the finite element method is not required. Our results are obtained using local Nitsche and Schatz-type error estimates, a weak version of Aubin-Nitsche duality lemma and a discrete inf-sup condition. These theoretical results are confirmed by numerical illustrations.

This paper develops a fully discrete modified characteristic finite element method for a coupled system consisting of the fully nonlinear Monge-Amp\'ere equation and a transport equation. The system is the Eulerian formulation in the dual space for the B. J. Hoskins' semigeostrophic flow equations, which are widely used in meteorology to model slowly varying flows constrained by rotation and stratification. To overcome the difficulty caused by the strong nonlinearity, we first formulate (at the differential level) a vanishing moment approximation of the semigeostrophic flow equations, a methodology recently proposed by the authors \cite{Feng1,Feng2}, which involves approximating the fully nonlinear Monge-Amp\'ere equation by a family of fourth order quasilinear equations. We then construct a fully discrete modified characteristic finite element method for the regularized problem. It is shown that under certain mesh and time stepping constraints, the proposed numerical method converges with an optimal order rate of convergence. In particular, the obtained error bounds show explicit dependence on the regularization parameter $\vepsi$. Numerical tests are also presented to validate the theoretical results and to gauge the efficiency of the proposed fully discrete modified characteristic finite element method.

This article is from Theoretical Biology & Medical Modelling , volume 10 . Abstract Background: The resistance of the bone against damage by repairing itself and adapting to environmental conditions is its most important property. These adaptive changes are regulated by physiological process commonly called the bone remodeling. Better understanding this process requires that we apply the theory of elastic-damage under the hypothesis of small displacements to a bone structure and see its mechanical behavior. Results: The purpose of the present study is to simulate a two dimensional model of a proximal femur by taking into consideration elastic-damage and mechanical stimulus. Here, we present a mathematical model based on a system of nonlinear ordinary differential equations and we develop the variational formulation for the mechanical problem. Then, we implement our mathematical model into the finite element method algorithm to investigate the effect of the damage. Conclusion: The results are consistent with the existing literature which shows that the bone stiffness drops in damaged bone structure under mechanical loading.

This article is from Progress in Orthodontics , volume 15 . Abstract Background: Orthodontic palatal expansion appliances have been widely used with satisfactory and, most often, predictable clinical results. Recently, clinicians have successfully utilized micro-implants with palatal expander designs to work as anchors to the palate to achieve more efficient skeletal expansion and to decrease undesired dental effects. The purpose of the study was to use finite element method (FEM) to determine the stress distribution and displacement within the craniofacial complex when simulated conventional and micro-implant-assisted rapid palatal expansion (MARPE) expansion forces are applied to the maxilla. The simulated stress distribution produced within the palate and maxillary buttresses in addition to the displacement and rotation of the maxilla could then be analyzed to determine if micro-implants aid in skeletal expansion. Methods: A three-dimensional (3D) mesh model of the cranium with associated maxillary sutures was developed using computed tomography (CT) images and Mimics modeling software. To compare transverse expansion stresses in rapid palatal expansion (RPE) and MARPE, expansion forces were distributed to differing points on the maxilla and evaluated with ANSYS simulation software. Results: The stresses distributed from forces applied to the maxillary teeth are distributed mainly along the trajectories of the three maxillary buttresses. In comparison, the MARPE showed tension and compression directed to the palate, while showing less rotation, and tipping of the maxillary complex. In addition, the conventional hyrax displayed a rotation of the maxilla around the teeth as opposed to the midpalatal suture of the MARPE. This data suggests that the MARPE causes the maxilla to bend laterally, while preventing unwanted rotation of the complex. Conclusions: In conclusion, the MARPE may be beneficial for hyperdivergent patients, or those that have already experienced closure of the midpalatal suture, who require palatal expansion and would worsen from buccal tipping of the teeth or maxillary complex.

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