自適應(yīng)計算

內(nèi)容概要

　　《自適應(yīng)計算：理論與算法（6）（英文版）》根據(jù)2005年在北京大學(xué)數(shù)學(xué)院舉行的暑期班的幾位主講教授的講稿組成。主要討論自適應(yīng)網(wǎng)格方法的程序﹑實現(xiàn)和理論基礎(chǔ)?！　蹲赃m應(yīng)計算：理論與算法（6）（英文版）》每章的作者均是這一領(lǐng)域的重要專家，內(nèi)容是近十年的一些新結(jié)果和新進展?！蹲赃m應(yīng)計算：理論與算法（6）（英文版）》和暑期班的目的是一致的，就是為了推動國內(nèi)外在這一重要領(lǐng)域的研究。

書籍目錄

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　BibliographyChapter 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　BibliographyChapter 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　BibliographyChapter 4 Convergence Theory of Moving Grid MethodsChapter 5 Computation of Crystalline Microstructures with The Mesh Transformation MethodChapter 6 On The Use of Moving Mesh Methods to Solve PEDsChapter 7 Theory and Application of Adaptive Moving Grid MethodsChapter 8 Recovery Techniques in Finite Element MethodsIndex

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