有限元方法选讲
2010-8
科学出版社
陈志明，武海军
162
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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．
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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书是正版的，很好~
很好的基础书~上课教材