Numerical Solution of Elliptic and Parabolic Partial Differential Equations

Numerical Solution of Elliptic and Parabolic Partial Differential Equations

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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 can be found on the accompanying CD-ROM).show more

Product details

  • Online resource
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 55 b/w illus. 13 colour illus. 300 exercises
  • 1139025503
  • 9781139025508

Table of contents

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 more

About John A. Trangenstein

John A. Trangenstein is Professor of Mathematics and Adjunct Professor of Civil and Environmental Engineering at Duke University, North Carolina, more

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