Adaptive numerical solution of PDEs / Peter Deuflhard, Martin Weiser.

Format:

Book

Author/Creator:

Deuflhard, P. (Peter)

Contributor:

Weiser, Martin.

Series:

De Gruyter Textbook

De Gruyter textbook

Language:

English

Subjects (All):

Differential equations, Elliptic--Numerical solutions--Textbooks.

Differential equations, Elliptic.

Differential equations, Parabolic--Numerical solutions--Textbooks.

Differential equations, Parabolic.

Physical Description:

1 online resource (436 p.)

Place of Publication:

Berlin : De Gruyter, c2012.

Language Note:

English

System Details:

Mode of access: World Wide Web.

Summary:

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.

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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9786613940964

9781283628518

1283628511

9783110283112

3110283115

OCLC:

812251506