有限元方法选讲
有限元方法选讲封面图

有限元方法选讲

陈志明, 武海军, 著

出版社:科学出版社

年代:2010

定价:35.0

书籍简介:

本书结合作者的科研成果,介绍了偏微分方程有限元方法中的若干经典及前沿专题。

书籍目录:

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

内容摘要:

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.

书籍规格:

书籍详细信息
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丛书名信息与计算科学丛书
9787030283382
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出版地北京出版单位科学出版社
版次1版印次1
定价(元)35.0语种简体中文
尺寸24 × 17装帧平装
页数 200 印数

书籍信息归属:

有限元方法选讲是科学出版社于2010.7出版的中图分类号为 O241.82 的主题关于 有限元法 的书籍。