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During the period covered by this grant, we conducted research on the development and application of adaptive numerical methods for singularly perturbed initial-boundary value problems for partial differential equations. We studied both local refinement methods and methods of lines techniques using properly nested and overlapping grids. The geometric modeling capabilities of our procedures were improved through the use of finite quadtree and octree encoding schemes; parallel versions of adaptive procedures on shared-memory computers were developed; and variable-order finite element methods to be used with adaptive p- and hp-refinement were created.