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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