有限元方法选讲

《有限元方法选讲(英文版)》内容简介：This book grows out of the lectures the first author gave in the summer of 2002 in the Institute of Computational Mathematics of Chinese Academy of Sciences．The purpose of the lectures was to present a concise introduction to the basic ideas and mathematical tools in the construction and analysis of finite element methods for solving partial differential equations So that the students can start to do research on the theory and applications of the finite element method after the summer course．Some of the materials of the book have been taught several times by the authors in Nanjing University and Peking University．The current form of the book is based on the lecture notes which are constantly updated and expanded reflecting the newest development of the topics through the years．

Preface Chapter1　VariationalFormulationofEllipticProblems 1.1　Basic concepts of Sobolev space 1.2　variationalformulation 1.3　Exercises Chapter2　FiniteElementMethodsforEllipticEquations 2.1　GalerkinmethodforvariationalprobleHIS 2.2　Theconstructionoffiniteelementspaces 2.2.1　ThefinReelemerit 2.3　Computationalconsideration 2.4 Exercises Chapter3　ConvergenceTheoryofFiniteElementMethods 3.1　InterpolationtheoryinSobolevspaces 3.2　Theenergyerrorestimate 3.3　TheL2errorestimate 3.4　Exercises Chapter4　AdaptiveFiniteElementMethods 4.1　Anexamplewithsingularity 4.2　Aposteriorierroranalysis 4.2.1　TheCldmentinterpolationoperator 4.2.2　Aposteriorierrorestimates 4.3　Adaptivealgorithm 4.4　Convergenceanalysis 4.5　Exercises Chapter5　FiniteElementMultigridMethods 5.1　Themodelproblem 5.2　Iterativemethods 5.3　ThemultigridV-cycle algorithm 5.4　ThefiniteelementmultigridV-cycle algorithm 5.5　Thefullmultigridandworkestimate 5.6　Theadaptivemultigridmethod 5.7　Exercises Chapter6　MixedFiniteElementMethods 6.1　Abstractframework 6.2　ThePoissonequationasamixedproblem 6.3　TheStokesproblem 6.4　Exercises Chapter7　FiniteElementMethOdsforParabolicProblems 7.1　Theweaksolutionsofparabolicequations 7.2　Thesemidiscreteapproximation 7.3　Thefullydiscreteapproximation 7.4　Aposteriorierroranalysis 7.5　Theadaptivealgorithm 7.6　Exercises Chapter 8　FiniteElementMethodsforMaxwellEquations 8.1　ThefunctionspaceH（curl；Ω) 8.2　Thecurlconformingfiniteelementapproximation 8.3　FiniteelementmethodsfortimeharmonicMaxwellequations 8.4　Aposteriorierroranalysis 8.5　Exercises Chapter 9　MultiscaleFiniteElementMethodsforEllipticEquations 9.1　Thehomogenizationresult 9.2　Themultiscalefiniteelementmethod 9.2.1　Errorestimatewhenh　　9.2.2　Errorestimatewhenh>? 9.3　Theover-sampling multiscale finite element method 9.4　Exercises Chapter10　Implementations 10.1　AbriefintroductiontotheMATLABPDET00lbox 10.1.1　Afirstexample-Poisson equation on the unit disk 10.1.2　Themeshdatastructure 10.1.3　Aquickreference 10.2　CodesforExample4.1－L-shaped domain problem on uniform meshes 10.2.1　Themainscript 10.2.2　H1error 10.2.3　Seven-point Gauss quadrature rule 10.3　CodesforExample4.6－L-shaped domain problem on adaptive meshes 10.4 ImplementationofthemultigridV-cycle algorithm 10.4.1　MatrixversionsforthemultigridV-cycle algorithm and FMG 10.4.2　CodeforFMG 10.4.3　CodeforthemultigridV-cycle algorithm 10.4.4　The“newest vertex bisection”algorithm for mesh refinements 10.5　Exercises Bibliography