Adaptive Numerical Solution of PDEs

Peter Deuflhard; Martin Weiser

Published by De Gruyter 2012

Adaptive Numerical Solution of PDEs

Peter Deuflhard and Martin Weiser

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110283112

Overview
Contents

About this book

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence.

Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted.

The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

Standard work on numerics of partial differential equations
Elementary and understandable presentation of the mathematical theory
Covers efficiency of numerical algorithms and scientific computing
Includes in-depth mathematical tools in the appendix

Author / Editor information

Peter Deuflhard and Martin Weiser, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Germany.

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Requires Authentication Unlicensed Licensed Download PDF	vii
Outline Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Elementary Partial Differential Equations Requires Authentication Unlicensed Licensed Download PDF	5
Chapter 2. Partial Differential Equations in Science and Technology Requires Authentication Unlicensed Licensed Download PDF	34
Chapter 3. Finite Difference Methods for Poisson Problems Requires Authentication Unlicensed Licensed Download PDF	62
Chapter 4. Galerkin Methods Requires Authentication Unlicensed Licensed Download PDF	86
Chapter 5. Numerical Solution of Linear Elliptic Grid Equations Requires Authentication Unlicensed Licensed Download PDF	143
Chapter 6. Construction of Adaptive Hierarchical Meshes Requires Authentication Unlicensed Licensed Download PDF	203
Chapter 7. Adaptive Multigrid Methods for Linear Elliptic Problems Requires Authentication Unlicensed Licensed Download PDF	246
Chapter 8. Adaptive Solution of Nonlinear Elliptic Problems Requires Authentication Unlicensed Licensed Download PDF	310
Chapter 9. Adaptive Integration of Parabolic Problems Requires Authentication Unlicensed Licensed Download PDF	333
A Appendix Requires Authentication Unlicensed Licensed Download PDF	380
B Software Requires Authentication Unlicensed Licensed Download PDF	398
Bibliography Requires Authentication Unlicensed Licensed Download PDF	401
Index Requires Authentication Unlicensed Licensed Download PDF	415

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate Students, PhD Students, and Lecturers in Mathematics, Physics, Engineering Sciences, Scientific Computing, and Applied Mathematics; Academic Libraries
Pages
- Front matter: 11
- Main content: 421
Illustrations
- Tables: 9
Keywords: Numerical Solution; Partial Differential Equation; Scientific Computing; Algorithm; Adaptive

eBook

Published: August 31, 2012
ISBN: 9783110283112

Hardcover

Published: August 17, 2012
ISBN: 9783110283105