有限元方法選講

內(nèi)容概要

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．

書籍目錄

PrefaceChapter1　VariationalFormulationofEllipticProblems　1.1　Basic concepts of Sobolev space　1.2　variationalformulation　1.3　ExercisesChapter2　FiniteElementMethodsforEllipticEquations　2.1　GalerkinmethodforvariationalprobleHIS　2.2　Theconstructionoffiniteelementspaces　　2.2.1　ThefinReelemerit　2.3　Computationalconsideration　2.4 ExercisesChapter3　ConvergenceTheoryofFiniteElementMethods　3.1　InterpolationtheoryinSobolevspaces　3.2　Theenergyerrorestimate　3.3　TheL2errorestimate　3.4　ExercisesChapter4　AdaptiveFiniteElementMethods　4.1　Anexamplewithsingularity　4.2　Aposteriorierroranalysis　　4.2.1　TheCldmentinterpolationoperator　　4.2.2　Aposteriorierrorestimates　4.3　Adaptivealgorithm　4.4　Convergenceanalysis　4.5　ExercisesChapter5　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　ExercisesChapter6　MixedFiniteElementMethods　6.1　Abstractframework　6.2　ThePoissonequationasamixedproblem　6.3　TheStokesproblem　6.4　ExercisesChapter7　FiniteElementMethOdsforParabolicProblems　7.1　Theweaksolutionsofparabolicequations　7.2　Thesemidiscreteapproximation　7.3　Thefullydiscreteapproximation　7.4　Aposteriorierroranalysis　7.5　Theadaptivealgorithm　7.6　ExercisesChapter 8　FiniteElementMethodsforMaxwellEquations　8.1　ThefunctionspaceH（curl；Ω)　8.2　Thecurlconformingfiniteelementapproximation　8.3　FiniteelementmethodsfortimeharmonicMaxwellequations　8.4　Aposteriorierroranalysis　8.5　ExercisesChapter 9　MultiscaleFiniteElementMethodsforEllipticEquations　9.1　Thehomogenizationresult　9.2　Themultiscalefiniteelementmethod　　9.2.1　Errorestimatewhenh

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