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 equa...

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《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
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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
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