Numerical solution of elliptic and parabolic partial differential equations
By: John A. Trangenstein
Publisher: Cambridge University Press; Brand: Cambridge University Press
Published: 2012
Place of publication: Cambridge; New York
Language: eng
Number of pages: 661
ISBN-13: 9780521877268
Subjects: Numerical solutions; Elliptic Differential equations; MATHEMATICS / General; Parabolic Differential equations
Description: "For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which is available online and on the accompanying CD-ROM)"--
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: Preface; 1. Introduction to partial differential equations; 2. Parabolic equations; 3. Iterative linear algebra; 4. Introduction to finite element methods; 5. Finite element theory; 6. Finite element approximations; 7. Mixed and hybrid finite elements; 8. Finite elements for parabolic equations; 9. Finite elements and multigrid; 10. Local refinement; Nomenclature; Bibliography; Author index; Subject index.