自适应计算

Chapter 1 Convergence of Adaptive Finite Element Methods

1.1 Involution

1.2 Preliminaries

1.3 Residual type error estimator

1.4 Convergence of an adaptive finite element method

1.5 Optimality of the adaptive finite element method

Bibliography

Chapter 2 A Posteriori Error Estimator by Post.Processing

2.1 Introduction

2.2 Linear finite element on patch symmetric grids

2.3 Linear finite element on mildly structured 2dds

2.4 Linear finite element on general unstructured grids

Bibliography

Chapter 3 Anisotropic Mesh Adaptation and Movement

3.1 Introduction

3.1.1 Sobolev spaces

3.1.2 Mesh terminology

3.1.3 Two algebraic inequalities

3.2 Basic principles in mesh adaptation

3.2.1 Geometric meaning of SVD decomposition

3.2.2 Alignment and equidistribution

3.2.3 Alignment and equidistribution for finite element meshes

3.3 Interpolation theory in Sobolev spaces

3.3.1 Finite element terminology

3.3.2 Element.Wise estimate on interpolation error

3.4 Isotropic error estimates

3.4.1 Chain rule

3.4.2 Isotropic error estimation on a general mesh

3.4.3 Error bound on regular triangulations

3.5 Anisotropic error estimates

3.5.1 An anlsotroplc error bound

3.5.2 Anisotropic error estimates independent of coordinate system

3.5.3 Bibliographic notes

3.6 Mesh quality measures and monitor functions

3.6.l Mesh quality measures

3.6.2 The isotropic case

3.6.3 The anisotropic case：J=1

3.6.4 The anisotropic case：2=2

3.7 Anisotropic mesh adaptation：Refinement approach

3.7.1 Metric tensor

3.7.2 Numerical experiments

3.8 Anisotropic mesh adoption：Variation approach

3.8.1 Functional for mesh alignment

3.8.2 Functional for equidistribution

3.8.3 Mesh adoption functional

3.8.4 Mesh equation

3.8.5 Numerical experiments

3.9 Adaptive moving mesh methods：MMPDE approach

3.9.1 The MMPDE method

3.9.2 Numerical examples

3.10 Adaptive moving mesh methods：GCL approach

3.10.1 GCL method

3.10.2 Relation to the Lagrange method and the deformation map Method

3.10.3 Choice of w，Vref，and P

3.10.4 Numerical examples

3.11 Conclusions

Bibliography

Chapter 4 Convergence Theory of Moving Grid Methods

Chapter 5 Computation of Crystalline Microstructures with The Mesh Transformation Method

Chapter 6 On The Use of Moving Mesh Methods to Solve PEDs

Chapter 7 Theory and Application of Adaptive Moving Grid Methods

Chapter 8 Recovery Techniques in Finite Element Methods

Index

《自适应计算：理论与算法（6）（英文版）》根据2005年在北京大学数学院举行的暑期班的几位主讲教授的讲稿组成。主要讨论自适应网格方法的程序﹑实现和理论基础。 《自适应计算：理论与算法（6）（英文版）》每章的作者均是这一领域的重要专家，内容是近十年的一些新结果和新进展。《自适应计算：理论与算法（6）（英文版）》和暑期班的目的是一致的，就是为了推动国内外在这一重要领域的研究。