This IMA Volume in Mathematics and its Applications GRID GENERATION AND ADAPTIVE ALGORITHMS is based on the proceedings of a workshop with the same title. The work­ shop was an integral part of the 1996-97 IMA program on "MATHEMAT­ ICS IN HIGH-PERFORMANCE COMPUTING. " I would like to thank Marshall Bern (Xerox, Palo Alto Research Cen­ ter), Joseph E. Flaherty (Department of Computer Science, Rensselaer Polytechnic Institute), and Mitchell Luskin (School of Mathematics, Uni­ versity of Minnesota), for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda­ tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr. , Professor and Director v PREFACE Scientific and engineering computation has become so complex that traditional numerical computation on uniform meshes is generally not pos­ sible or too expensive. Mesh generation must reflect both the domain geometry and the expected solution characteristics. Meshes should, fur­ thermore, be related to the solution through computable estimates of dis­ cretization errors. This, suggests an automatic and adaptive process where an initial mesh is enriched with the goal of computing a solution with prescribed accuracy specifications in an optimal manner. While automatic mesh generation procedures and adaptive strategies are becoming available, major computational challenges remain. Three-dimensional mesh genera­ tion is still far from automatic.

hp-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation.- Tetrahedral bisection and adaptive finite elements.- Resolution of boundary layers on triangular meshes.- A general concept of adaptivity in finite element methods with applications to problems in fluid and structural mechanics.- A solution based H1 norm triangular mesh quality indicator.- Experiments with repartitioning and load balancing adaptive meshes.- Distributed octree data structures and local refinement method for the parallel solution of three-dimensional conservation laws.- Adaptive finite element methods for elastostatic contact problems.- The full domain partition approach to parallel adaptive refinement.- Adaptive solution of phase change problems over unstructured tetrahedral meshes.