Operator Theory and Numerical Methods

Hiroshi Fujita, Norikazu Saito and Takashi Suzuki (Eds.)9780444504746, 0444504745

In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed. In 1991 an article on the finite element method applied to evolutionary problems was published. Following the method, basically this book studies various schemes from operator theoretical points of view. Many parts are devoted to the finite element method, but other schemes and problems (charge simulation method, domain decomposition method, nonlinear problems, and so forth) are also discussed, motivated by the observation that practically useful schemes have fine mathematical structures and the converses are also true. This book has the following chapters: 1. Boundary Value Problems and FEM. 2. Semigroup Theory and FEM. 3. Evolution Equations and FEM. 4. Other Methods in Time Discretization. 5. Other Methods in Space Discretization. 6. Nonlinear Problems. 7. Domain Decomposition Method.

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Table of contents :
Content:
Preface
Page v
Hiroshi Fujita, Norikazu Saito, Takashi Suzuki

Chapter 1 Elliptic boundary value problems and FEM Original Research Article
Pages 1-46

Chapter 2 Semigroup theory and FEM Original Research Article
Pages 47-94

Chapter 3 Evolution equations and FEM Original Research Article
Pages 95-144

Chapter 4 Other methods in time discretization Original Research Article
Pages 145-170

Chapter 5 Other methods in space discretization Original Research Article
Pages 171-206

Chapter 6 Nonlinear problems Original Research Article
Pages 207-242

Chapter 7 Domain decomposition method Original Research Article
Pages 243-273

Bibliography
Pages 275-302

Index
Pages 303-309