Adaptive Numerical Solution of PDEs / / Peter Deuflhard, Martin Weiser.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Deuflhard, Peter,; Weiser, Martin,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (421 p.)

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.

Table of Contents

Frontmatter -- Preface -- Contents -- Outline -- Chapter 1. Elementary Partial Differential Equations -- Chapter 2. Partial Differential Equations in Science and Technology -- Chapter 3. Finite Difference Methods for Poisson Problems -- Chapter 4. Galerkin Methods -- Chapter 5. Numerical Solution of Linear Elliptic Grid Equations -- Chapter 6. Construction of Adaptive Hierarchical Meshes -- Chapter 7. Adaptive Multigrid Methods for Linear Elliptic Problems -- Chapter 8. Adaptive Solution of Nonlinear Elliptic Problems -- Chapter 9. Adaptive Integration of Parabolic Problems -- A Appendix -- B Software -- Bibliography -- Index