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
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