Adaptive grid methods are among the most important classes of numerical methods for partial differential equations that arise from scientific and engineering computing. The study of this type of methods has been very active in recent years for algorithm design， theoretical analysis and applications to practical computations. This volume contains a number of self-contained articles for adaptive finite element and finite difference methods， which is aimed to provide some introduction materials for graduate students and junior researchers and a collection of references for researchers and practitioners.These articles mostly grew out of the lectures notes that were given in Summer Workshops on Adaptive Method， Theory and Application organized by Tao Tang， Jinchao Xu and Pingwen Zhang in Peking University， China， during June 20：August 20， 2005. This summer school was aimed to provide a comprehensive and up-to-date presentation of modern theories and practical applications for adaptive computations. The main lecturers of the Summer School include Weizhang Huang of University of Kansas， Natalia Kopteva of University of Limerick， Zhiping Li of Peking University， John Mackenzie of Strathclyde University， Jinchao Xu of Penn State University， Paul Zegeling of Utrecht University， and Zhimin Zhang of Wayne State University. Other lecturers include Tao Tang， Xiaoping Wang of HKUST， Huazhong Tang and Pingwen Zhang （both from Peking University）. More detailed information of this summer school can be found in http：//ccse.pku.edu.cn/activities/2005/adaptiveseminar.htm（which is most in Chinese）.
作者簡介
暫缺《自適應(yīng)計算：理論與算法（英文版）》作者簡介
圖書目錄
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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