This self-contained book, the first in a two-part series on hp-adaptive finite elements by Leszek Demkowicz, describes 1D and 2D finite element codes and automatic hp-adaptivity strategies that are designed to deliver meshes in the full range of error levels. The book first considers standard 1D elliptic problems and a 1D wave propagation problem. The author proceeds to discuss 2D elliptic problems, examining two model problems that are slightly beyond standard-level examples. He also includes an entire chapter on geometric modeling and mesh generation. The book then focuses on 2D time-harmonic Maxwell equations. A companion CD-ROM containing 1D and 2D codes accompanies the text.
Zusammenfassung
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 implementat
Inhalt
1D Model Elliptic Problem. Galerkin Method. 1D hp Finite Element Method. 1D hp Code. Mesh Refinements in 1D. Automatic hp Adaptivity in 1D. Wave Propagation Problems. 2D Elliptic Boundary-Value Problem. Sobolev Spaces. 2D hp Finite Element Method on Regular Meshes. 2D hp Code. Geometric Modeling and Mesh Generation. The hp Finite Element Method on h-Refined Meshes. Automatic hp Adaptivity in 2D. Examples of Applications. Exterior Boundary-Value Problems. 2D Maxwell Equations. Edge Elements and the de Rham Diagram. 2D Maxwell Code. hp Adaptivity for Maxwell Equations. Exterior Maxwell Boundary-Value Problems. A Quick Summary and Outlook. Appendix. Bibliography. Index.