- 有限元方法的数学理论(第3版)
- - 作者：(美)布雷
  - 出版社：世界图书出版公司
  - ISBN：9787510027437
  - 出版日期：2010/09/01
  - 页数：397
- 售价：22

内容大纲
作者介绍
目录
Series Preface
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
0 Basic Concepts
  0.1 Weak Formulation of Boundary Value Problems
  0.2 Ritz-Galerkin Approximation
  0.3 Error Estimates
  0.4 Piecewise Polynomial Spaces - The Finite Element Method
  0.5 Relationship to Difference Methods
  0.6 Computer Implementation of Finite Element Methods
  0.7 Local Estimates
  0.8 Adaptive Approximation
  0.9 Weighted Norm Estimates
  0.x Exercises
1 Sobolev Spaces
  1.1 Review of Lebesgue Integration Theory
  1.2 Generalized (Weak) Derivatives
  1.3 Sobolev Norms and Associated Spaces
  1.4 Inclusion Relations and Sobolev's Inequality
  1.5 Review of Chapter 0
  1.6 Trace Theorems
  1.7 Negative Norms and Duality
  1.x Exercises
2 Variational Formulation of Elliptic Boundary Value Problems
  2.1 Inner-Product Spaces
  2.2 Hilbert Spaces
  2.3 Projections onto Subspaces
  2.4 Riesz Representation Theorem
  2.5 Formulation of Symmetric Variational Problems
  2.6 Formulation of Nonsymmetric Variational Problems
  2.7 The Lax-Milgram Theorem
  2.8 Estimates for General Finite Element Approximation
  2.9 Higher-dimensional Examples
  2.x Exercises
3 The Construction of a Finite Element Space
  3.1 The Finite Element
  3.2 Triangular Finite Elements
     The Lagrange Element
     The Hermite Element
     The Argyris Element
  3.3 The Interpolant
  3.4 Equivalence of Elements
  3.5 Rectangular Elements
     Tensor Product Elements
     The Serendipity Element
  3.6 Higher-dimensional Elements
  3.7 Exotic Elements
  3.x Exercises
4 Polynomial Approximation Theory in Sobolev Spaces

  4.1 Averaged Taylor Polynomials
  4.2 Error Representation
  4.3 Bounds for Riesz Potentials
  4.4 Bounds for the Interpolation Error
  4.5 Inverse Estimates
  4.6 Tensor-product Polynomial Approximation
  4.7 Isoparametric Polynomial Approximation
  4.8 Interpolation of Non-smooth Functions
  4.9 A Discrete Sobolev Inequality
  4.x Exercises
5 n-Dimensional Variational Problems
  5.1 Variational Formulation of Poisson's Equation
  5.2 Variational Formulation of the Pure Neumann Problem
  5.3 Coercivity of the Variational Problem
  5.4 Variational Approximation of Poisson's Equation
  5.5 Elliptic Regularity Estimates
  5.6 General Second-Order Elliptic Operators
  5.7 Variational Approximation of General Elliptic Problems
  5.8 Negative-Norm Estimates
  5.9 The Plate-Bending Biharmonic Problem
  5.x Exercises
6 Finite Element Multigrid Methods
  6.1 A Model Problem
  6.2 Mesh-Dependent Norms
  6.3 The Multigrid Algorithm
  6.4 Approximation Property
  6.5 W-cycle Convergence for the kth Level Iteration
  6.6 P-cycle Convergence for the kth Level Iteration
  6.7 Full Multigrid Convergence Analysis and Work Estimates
  6.x Exercises
7 Additive Schwarz Preconditioners
  7.1 Abstract Additive Schwarz Framework
  7.2 The Hierarchical Basis Preconditioner
  7.3 The BPX Preconditioner
  7.4 The Two-level Additive Schwarz Preconditioner
  7.5 Nonoverlapping Domain Decomposition Methods
  7.6 The BPS Preconditioner
  7.7 The Neumann-Neumann Preconditioner
  7.8 The BDDC Preconditioner
  7.x Exercises
8 Max-norm Estimates
  8.1 Main Theorem
  8.2 Reduction to Weighted Estimates
  8.3 Proof of Lemma 8.2.6
  8.4 Proofs of Lemmas 8.3.7 and 8.3.11
  8.5 Lp Estimates (Regular Coefficients)
  8.6 Lp Estimates (Irregular Coefficients)
  8.7 A Nonlinear Example
  8.x Exercises
9 Adaptive Meshes

  9.1 A priori Estimates
  9.2 Error Estimators
  9.3 Local Error Estimates
  9.4 Estimators for Linear Forms and Other Norms
  9.5 A Convergent Adaptive Algorithm
  9.6 Conditioning of Finite Element Equations
  9.7 Bounds on the Condition Number
  9.8 Applications to the Conjugate-Gradient Method
  9.x Exercises
10 Variational Crimes
  10.1 Departure from the Framework
  10.2 Finite Elements with Interpolated Boundary Conditions
  10.3 Nonconforming Finite Elements
  10.4 Isoparametric Finite Elements
  10.5 Discontinuous Finite Elements
  10.6 Poincare-Friedrichs Inequalitites for Piecewise Wp1 Functions
  10.x Exercises
11 Applications to Planar Elasticity
  11.1 The Boundary Value Problems
  11.2 Weak Formulation and Korn's Inequality
  11.3 Finite Element Approximation and Locking
  11.4 A Robust Method for the Pure Displacement Problem
  11.x Exercises
12 Mixed Methods
  12.1 Examples of Mixed Variational Formulations
  12.2 Abstract Mixed Formulation
  12.3 Discrete Mixed Formulation
  12.4 Convergence Results for Velocity Approximation
  12.5 The Discrete Inf-Sup Condition
  12.6 Verification of the Inf-Sup Condition
  12.x Exercises
13 Iterative Techniques for Mixed Methods
  13.1 Iterated Penalty Method
  13.2 Stopping Criteria
  13.3 Augmented Lagrangian Method
  13.4 Application to the Navier-Stokes Equations
  13.5 Computational Examples
  13.x Exercises
14 Applications of Operator-Interpolation Theory
  14.1 The Real Method of Interpolation
  14.2 Real Interpolation of Sobolev Spaces
  14.3 Finite Element Convergence Estimates
  14.4 The Simultaneous Approximation Theorem
  14.5 Precise Characterizations of Regularity
  14.x Exercises
References
Index

内容大纲

作者介绍

目录

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