| 《有限元方法选讲(英文版)》是由科学出版社出版的。 |
| 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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