偏微分方程的数值近似法

书籍目录

Part I.Basic Concepts and Methods for PDEs‘ Approximation   1. Introduction     1.1 The Conceptual Path Behind the Approximation     1.2 Preliminary Notation and Function Spaces     1.3 Some Results About Sobolev Spaces     1.4 Comparison Results   2. Numerical Solution of Linear Systems     2.1 Direct Methods    2.2 Generalities on Iterative Methods     2.3 Classical Iterative Methods     2.4 Modern Iterative Methods     2.5 Preconditioning    2.6 Conjugate Gradient and Lanczos like Methods for Non-Symmetric Problems    2.7 The Multi-Grid Method    2.8 Complements  3.Finite Element Approximation    3.1 Triangulation    3.2 Piecewise-Polynomial Subspaces    3.3 Degrees of Freedom and Shape Functions    3.4 The Interpolation Operator    3.5 Projection Opeators    3.6 Complements  4.Polynomial Approximation    4.1 Orthogonal Polynomials    4.2 Gaussian Quadrature and Interpolation    4.3 Chebyshev Expansion    4.4 Legendre Expansion    4.5 Two-Dimensional Extensions    4.6 Complements  5.Galerkin,Collocation and Other Methods    5.1 An Abstract Reference Boundary Value Problem    5.2 Galerkin Method    5.3 Petrov-Galerkin Method    ……Part Ⅱ.Approximation of Boundary Value Problems  6.Elliptic Problems:Approximation by Galerkin and Collocation Methods  7.Elliptic Prblems:Approximation by Mixed and Hybrid Methods  8.Steady Advection-Diffusion-Problems  9.The Stokes Problem  10.The Steady Navier-Stokes ProblemPart Ⅲ.Approximation of Initial-Boundary Value Problems  11.Parabolic Problems  12.Unsteady Advection-Diffusion Problems  13.The Unsteady Navier-Stokes Problem  14.Hyperbolic ProblemsReferencesSubject Index

作者简介

This is a book on the numerical approximation of partial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation.



　　本书为英文版。

图书封面

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