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內容簡介

　　《有限元方法（英文版）》係統地論述瞭有限元方法的數學基礎理論。以橢圓偏微分方程邊值問題為例，介紹瞭協調有限元方法以及非協調等非標準有限元方法的數學描述、收斂條件和性質、有限元解的先驗和後驗誤差估計以及有限元空間的基本性質，其中包括作者多年來的部分研究成果。

內頁插圖

目錄

Preface to the Series in Information and Computational Science
Preface
Chapter 1Variational Principle
1.1 Sobolev Space
1.2 Poisson Equation
1.2.1 Dirichlet Problem
1.2.2 Neumann Problem
1.3 Biharmonic Equation
1.4 Abstract Variational Problem
1.5 Galerkin Method and Ritz Method

Chapter 2 Finite Element and Finite Element Space
2.1 Triangulation
2.2 Finite Element
2.3 Finite Element Space
2.4 Second Order Problem: Simplex Elements
2.4.1 Simplex Element of Degreek
2.4.2 Linear Simplex Element
2.4.3 Quadric Simplex Element
2.4.4 Cubic Simplex Element
2.4.5 Incomplete Cubic Simplex Element
2.4.6 Crouzeix-Raviart Element
2.4.7 Cubic Hermite Simplex Element
2.4.8 Zienkiewicz Element
2.5 Second Order Problem: Rectangle Elements
2.5.1 Rectangle Element of Type(k)
2.5.2 Incomplete Rectangle Element of Type(2)
2.5.3 Wilson Element
2.5.4 Rectangle C-R Element
2.6 Fourth Order Problem: Simplex Elements
2.6.1 Morley Element
2.6.2 Zienkiewicz Element
2.6.3 Morley-Zienkiewicz Element
2.6.4 Modified Zienkiewicz Element
2.6.5 12-parameter Triangle Plate Element
2.6.6 15-parameter Triangle Plate Element
2.6.7 Argyris Element
2.6.8 Bell Element
2.6.9 Cubic Tetrahedron Element
2.7 Fourth Order Problem: Rectangle Elements
2.7.1 Rectangle Morley Element
2.7.2 Adini Element
2.7.3 Bogner-Fox-Schmit Element
2.8 2m-th Order Problem: MWX Element

Chapter 3 Interpolation Theory of Finite Elements
3.1 Affine Mapping and Affine Family
3.2 Affine Continuity and Scale Invariance
3.3 Interpolation Error
3.4 Inverse Inequality
3.5 Approximate Error of Finite Element Spaces
3.6 Interpolation Error of General Element

Chapter 4 Conforming Finite Element Method
4.1 Poisson Equation
4.2 Plate Bending Problem
4.3 A Posteriori Error Estimate

Chapter 5 Nonconforming Finite Element Methods
5.1 Nonconforming Finite Element
5.2 Weak Continuity
5.3 Second Order Elliptic Problem
5.4 Fourth Order Elliptic Problem
5.5 2m-th Order Elliptic Problem
5.6 A Posteriori Error Estimate
5.7 Error Estimate in L2 Norm

Chapter 6 Convergence of Nonconforming Finite Element
6.1 Generalized Path Test
6.2 Patch Test
6.2.1 Patch Test
6.2.2 Weak Patch Test
6.2.3 Sufficiency of Patch Test
6.2.4 Necessity of Patch Test
6.3 Counter Examples of Patch Test
6.4 F-E-M Test
……

Chapter 7 Quasi-Conforming Element Method
Chapter 8 Unconventional Finite Element Method
Chapter 9 Double Set Parameter Method
Chapter 10 Property of Finite Element Space
Chapter 11 L∞ Error Estimate for Second Order Problem
Chapter 12 L∞ Error Estimate for Plate Bending Problem
Bibliography
Index

前言/序言

　　The finite element method has achieved a great deal of success in many fields since itwas first suggested in the structural analysis in the fifth decade oflast century.　Todayit is a powerful numerical tool solving partial differential equations. The scholars inour country contributed much to the foundation and development of finite elementmethod. Feng's work is original, independent of the West, to the foundation of thefinite element method.
　　The basic idea of the finite element method is using discrete solutions on finiteelement spaces to approximate the continuous solutions on infinite dimensional space V according to the variational principle.　The typical steps of constructing finiteelement spaces are the following.
　　(1) The domain S2, the continuous solution defined on, is subdivided into somesubdomains, which are called elements.
　　(2) On each element, an m-dimensional polynomial space and m nodal parame-ters are selected, such that each polynomial in the space is determined uniquely bya group of nodal parameters. The function values and derivatives at some points onthe element are often taken as the nodal parameters.
　　(3) A piecewise polynomial space Vh. on domain l2, called finite element space,is obtained by linking the nodal parameters on elements in some way.
　　For the mathematical foundation of the finite element method, there is a well-known result:
　　The approximation of jinite elefme,nt solutioln to the treal solution is dependenton the approximation of jVnite element space Vh, to the space V, provided Vt is asubspace of V.
　　The approximate property of the finite element spaces can be dealt with by theinterpolation theory of the finite elements.
有限元方法（英文版） [Finite Element Methods] 下載 mobi epub pdf txt 電子書

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