Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell ProblemsOffering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementat |
Contents
Chapter 1 1D Model Elliptic Problem | 3 |
Chapter 2 Galerkin Method | 33 |
Chapter 3 1D hp Finite Element Method | 41 |
Chapter 4 1D hp Code | 57 |
Chapter 5 Mesh Refinements in 1D | 71 |
Chapter 6 Automatic hp Adaptivity in 1D | 95 |
Chapter 7 Wave Propagation Problems | 117 |
Part II 2D Elliptic Problems | 133 |
Chapter 15 Examples of Applications | 241 |
Chapter 16 Exterior BoundaryValue Problems | 259 |
Part III 2D Maxwell Problems | 283 |
Chapter 17 2D Maxwell Equations | 285 |
Chapter 18 Edge Elements and the de Rham Diagram | 301 |
Chapter 19 2D Maxwell Code | 323 |
Chapter 20 hp Adaptivity for Maxwell Equations | 337 |
Chapter 21 Exterior Maxwell BoundaryValue Problems | 351 |
Chapter 8 2D Elliptic BoundaryValue Problem | 135 |
Chapter 9 Sobolev Spaces | 149 |
Chapter 10 2D hp Finite Element Mehtod on Regular Meshes | 163 |
Chapter 11 2D hp Code | 185 |
Chapter 12 Geometric Modeling and Mesh Generation | 195 |
Chapter 13 The hp Finite Element Method on hRefined Meshes | 211 |
Chapter 14 Automatic hp Adaptivity in 2D | 227 |
Chapter 22 A Quick Summary and Outlook | 369 |
Appendix A Construction of makefile | 371 |
| 375 | |
| 389 | |
Back cover | 399 |
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Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional ... Leszek Demkowicz No preview available - 2006 |
Common terms and phrases
adaptivity algorithm approximation error basis functions bilinear form boundary conditions Cauchy coarse grid coefficients component compute constant constrained nodes convergence history coordinates corresponding curl data structure arrays defined denotes determine Dirichlet BC discrete discussed domain element d.o.f. element edges element matrices element shape functions element sons error estimate exact solution Exercise Figure finite element finite element method flag frontal solver Galerkin method global gradient grid solution h refinements H(curl H(curl)-conforming Helmholtz equation hp algorithm hp-adaptive infinite integration interface interpolation error linear load vector master element Maxwell equations Maxwell problems mdle middle node midedge modified element Neumann norm nrdof operator order of approximation parametrization plane wave polynomials of order projection-based interpolation quad rectangle seminorm Sobolev spaces solve stiffness matrix test functions theorem tion triangle vanish variational formulation vertex nodes zero αξ ди