Operator Theory and Numerical Methods
- 1st Edition, Volume 30 - August 31, 2011
- Latest edition
- Authors: H. Fujita, N. Saito, T. Suzuki
- Language: English
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… Read more
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.
Students, R&D for experts, Engineers
Chapter 1. Elliptic Boundary Value Problems and FEM1.1 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 FEM2.1 Evolutionary Problems 2.2 Semi-discretization 2.3 Fractional Powers 2.4 Full-discretization 2.5 Inhomogeneous Equation 2.6 Higher Accuracy 2.7 Loo Estimate 2.8 Hyperbolic Equation.Chapter 3. Evolution Equations and FEM3.1 Generation Theories3.2 A Priori Estimates 3.3 Semi-discretization 3.4 Full-discretization 3.5 Alternative Approach.Chapter 4. Other Methods in Time Discretization4.1 Rational Approximation of Semigroups4.2 Multi-step Method4.3 Product Formula.Chapter 5. Other Methods in Space Discretization5.1 Lumping of Mass5.2 Upwind Finite Elements5.3 Mixed Finite Elements5.4 Boundary Element Methods (BEM)5.5 Charge Simulation Methods (CSM).Chapter 6. Nonlinear Problems6.1 Semilinear Elliptic Equations6.2 Semilinear Parabolic Equations6.3 Degenerate Parabolic Equations.Chapter 7. Domain Decomposition Method7.1 Dirichlet to Neumann (DN) Map7.2 Dirichlet to Neumann (DN) Iteration7.3 Dirichlet2 to Neumann2 (DD-NN) Iteration7.4 Robin to Robin Iteration7.5 Exterior Problem7.6 The Stokes System.Bibliography. Index
- Edition: 1
- Latest edition
- Volume: 30
- Published: August 31, 2011
- Language: English
HF
H. Fujita
Affiliations and expertise
Tokai University, The Research Institute of Educational Development, Tokyo, JapanNS
N. Saito
Affiliations and expertise
Toyama University, Faculty of Education, Toyama, JapanTS
T. Suzuki
Affiliations and expertise
Osaka University, Department of Mathematics, Graduate School of Science, Toyonaka, JapanRead Operator Theory and Numerical Methods on ScienceDirect