Operator Theory and Numerical Methods
- H. Fujita, Tokai University, The Research Institute of Educational Development, Tokyo, Japan
- N. Saito, Toyama University, Faculty of Education, Toyama, Japan
- T. Suzuki, Osaka University, Department of Mathematics, Graduate School of Science, Toyonaka, Japan
Students, R&D for experts, Engineers
- Published: July 2001
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-50474-6
The authors provide a very sharp theoretical study of numerical methods used to solve partial diferential equations of elliptic and parabolic type. Every numerical scheme is thoroughly dissected. As a whole, everything fits together in a harmonious way.
Calin Ioan Gheorghiu, Zentrallblatt fur Mathematik
The book is efficiently organized and each chapter concludes with a very informative commentary section that provides brief but useful historical, bibliographical or technical comments.
Charles W. Groetsch, Mathematical Reviews
Table of ContentsChapter 1. Elliptic Boundary Value Problems and FEM
1.1 Elliptic Boundary Value Problems
1.2 Ritz-Galerkin Method
1.3 Finite Element Method (FEM)
1.4 Inverse Assumption
1.5 Loo Estimate
1.6 Lp Estimate
1.7 Asymptotic Expansion.
Chapter 2. Semigroup Theory and FEM
2.1 Evolutionary Problems
2.3 Fractional Powers
2.5 Inhomogeneous Equation
2.6 Higher Accuracy
2.7 Loo Estimate
2.8 Hyperbolic Equation.
Chapter 3. Evolution Equations and FEM
3.1 Generation Theories
3.2 A Priori Estimates
3.5 Alternative Approach.
Chapter 4. Other Methods in Time Discretization
4.1 Rational Approximation of Semigroups
4.2 Multi-step Method
4.3 Product Formula.
Chapter 5. Other Methods in Space Discretization
5.1 Lumping of Mass
5.2 Upwind Finite Elements
5.3 Mixed Finite Elements
5.4 Boundary Element Methods (BEM)
5.5 Charge Simulation Methods (CSM).
Chapter 6. Nonlinear Problems
6.1 Semilinear Elliptic Equations
6.2 Semilinear Parabolic Equations
6.3 Degenerate Parabolic Equations.
Chapter 7. Domain Decomposition Method
7.1 Dirichlet to Neumann (DN) Map
7.2 Dirichlet to Neumann (DN) Iteration
7.3 Dirichlet2 to Neumann2 (DD-NN) Iteration
7.4 Robin to Robin Iteration
7.5 Exterior Problem
7.6 The Stokes System.