数字方法为椭圆和抛物面偏微分方程 Numerical methods for elliptic and parabolic partial differential equations
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作者： Peter Knabner著
出 版 社： Oversea Publishing House
出版时间： 2003-6-1字数：版次： 1页数： 424印刷时间： 2003/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387954493包装： 精装内容简介
This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation. The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems. Detailed illustrations and extensive exercises are included. It will provide mathematics students with an introduction to the theory and methods, guiding them in their selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it will provide a general framework for formulation and analysis of methods providing a broader perspective to specific applications.
目录
Series Preface
Preface to the English Edition
Preface to the German Edition
For Example: Modelling Processes in Porous Media with Differential Equations
1 For the Beginning: The Finite Difference Method for the Poisson Equation
2 The Finite Element Method for the Poisson Equation
3 The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order
4 Grid Generation and A Posteriori Error Estimation
5 Iterative Methods for Systems of Linear Equations
6 The Finite Volume Method
7 Discretization Methods for Parabolic Initial Boundary Value Problems
8 Iterative Methods for Nonlinear Equations
9 Discretization Methods for Convection-Dominated Problems
A Appendices
A.1: Notation
A.2 Basic Concepts of Analysis
A.3 Basic Concepts of Linear Algebra
A.4 Some Definitions and Arguments of Linear Functional Analysis
A.5 Function Spaces
References: Textbooks and Monographs
References: Journal Papers
Index
