Grid Generation and Adaptive Algorithms

1. Front Matter

   Pages i-ix

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2. hp-Finite Element Procedures on Non-Uniform Geometric Meshes: Adaptivity and Constrained Approximation

   • Mark Ainsworth, Bill Senior

   Pages 1-27

3. Tetrahedral Bisection and Adaptive Finite Elements

   • Douglas N. Arnold, Arup Mukherjee

   Pages 29-42

4. Resolution of Boundary Layers on Triangular Meshes

   • Timothy J. Baker

   Pages 43-49

5. A General Concept of Adaptivity in Finite Element Methods with Applications to Problems in Fluid and Structural Mechanics

   • Roland Becker, Rolf Rannacher

   Pages 51-75

6. A Solution Based H ¹ Norm Triangular Mesh Quality Indicator

   • M. Berzins

   Pages 77-88

7. Experiments with Repartitioning and Load Balancing Adaptive Meshes

   • Rupak Biswas, Leonid Oliker

   Pages 89-111

8. Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of Three-Dimensional Conservation Laws

   • J. E. Flaherty, R. M. Loy, M. S. Shephard, M. L. Simone, B. K. Szymanski, J. D. Teresco et al.

   Pages 113-134

9. Adaptive Finite Element Methods for Elastostatic Contact Problems

   • Peter Hansbo, Claes Johnson

   Pages 135-149

10. The Full Domain Partition Approach to Parallel Adaptive Refinement

    • William F. Mitchell

    Pages 151-161

11. Adaptive Solution of Phase Change Problems Over Unstructured Tetrahedral Meshes

    • R. H. Nochetto, A. Schmidt, C. Verdi

    Pages 163-181

12. Back Matter

    Pages 182-189

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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.

• Partition
• Volume
• algorithms
• complexity
• computation
• data structure
• data structures
• finite element method
• form
• knowledge
• layers
• load balancing
• mechanics
• object
• variable
• combinatorics
• algorithm analysis and problem complexity

• Xerox Palo Alto Research Center, Palo Alto, USA

  Marshall W. Bern

• Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, USA

  Joseph E. Flaherty

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Mitchell Luskin

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