# Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

CRC Press, Oct 25, 2006 - Science - 398 pages
Offering 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 implementation of hp-adaptive FE methods, focusing on projection-based interpolation and the corresponding hp-adaptive strategy.

The book is split into three parts, progressing from simple to more advanced problems. Part I examines the hp elements for the standard 1D model elliptic problem. The author develops the variational formulation and explains the construction of FE basis functions. The book then introduces the 1D code (1Dhp) and automatic hp adaptivity. This first part ends with a study of a 1D wave propagation problem. In Part II, the book proceeds to 2D elliptic problems, discussing two model problems that are slightly beyond standard-level examples: 3D axisymmetric antenna problem for Maxwell equations (example of a complex-valued, indefinite problem) and 2D elasticity (example of an elliptic system). The author concludes with a presentation on infinite elements - one of the possible tools to solve exterior boundary-value problems. Part III focuses on 2D time-harmonic Maxwell equations. The book explains the construction of the hp edge elements and the fundamental de Rham diagram for the whole family of hp discretizations. Next, it explores the differences between the elliptic and Maxwell versions of the 2D code, including automatic hp adaptivity. Finally, the book presents 2D exterior (radiation and scattering) problems and sample solutions using coupled hp finite/infinite elements.

In Computing with hp-ADAPTIVE FINITE ELEMENTS, the information provided, including many unpublished details, aids in solving elliptic and Maxwell problems.

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### 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 Bibliography 375 Index 389 Back cover 399 Copyright