有限元方法选讲（英文版）

　　Preface
　　Chapter1VariationalFormulationofEllipticProblems
　　1.1 Basic concepts of Sobolev space
　　1.2 variationalformulation
　　1.3 Exercises
　　Chapter2FiniteElementMethodsforEllipticEquations
　　2.1 GalerkinmethodforvariationalprobleHIS
　　2.2 Theconstructionoffiniteelementspaces
　　2.2.1 ThefinReelemerit
　　2.3 Computationalconsideration
　　2.4 Exercises
　　Chapter3ConvergenceTheoryofFiniteElementMethods
　　3.1 InterpolationtheoryinSobolevspaces
　　3.2 Theenergyerrorestimate
　　3.3 TheL2errorestimate
　　3.4 Exercises
　　Chapter4AdaptiveFiniteElementMethods
　　4.1 Anexamplewithsingularity
　　4.2 Aposteriorierroranalysis
　　4.2.1 TheCldmentinterpolationoperator
　　4.2.2 Aposteriorierrorestimates
　　4.3 Adaptivealgorithm
　　4.4 Convergenceanalysis
　　4.5 Exercises
　　Chapter5FiniteElementMultigridMethods
　　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
　　Chapter6MixedFiniteElementMethods
　　6.1 Abstractframework
　　6.2 ThePoissonequationasamixedproblem
　　6.3 TheStokesproblem
　　6.4 Exercises
　　Chapter7FiniteElementMethOdsforParabolicProblems
　　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?
　　9.3 Theover-sampling multiscale finite element method
　　9.4 Exercises
　　Chapter10Implementations
　　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

　　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．