Preface to the Series in Information and Computational Science Preface Chapter 1 Variational 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 Degree k 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 Affne Mapping and Affne Family 3.2 Affne 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 L^2 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 Suffciency of Patch Test 6.2.4 Necessity of Patch Test 6.3 Counter Examples of Patch Test 6.4 F-E-M Test 6.4.1 F_1-Test 6.4.2 F_2-Test 6.4.3 E_1-M_1-Test 6.4.4 E_2-M_2-Test 6.4.5 Procedure of F-E-M Test 6.4.6 Quadrilateral Wilson element 6.4.7 8-parameter quadrilateral element 6.4.8 15-parameter triangle plate element 6.5 Superapproximation 6.6 Strange Convergence Behaviour 6.6.1 Second Carey Example 6.6.2 Zienkiewicz element Chapter 7 Quasi-Conforming Element Method 7.1 Second Order Problem:RQC4 Element 7.2 Biharmonic Equation 7.2.1 TQC9 Element 7.2.2 TQC12 Element 7.2.3 TQC15 Element 7.2.4 RQC12 Element 7.2.5 Three Dimensional Case:TQC16 Element 7.3 Rank Condition 7.4 Approximation 7.5 Error Estimate 7.6 A Posteriori Error Estimate Chapter 8 Unconventional Finite Element Method 8.1 Free Formulation Scheme 8.2 Two Finite Elements 8.2.1 TRUNC Element 8.2.2 Bergan Element 8.3 Convergence Analysis 8.4 General Situation 8.5 A Posteriori Error Estimate Chapter 9 Double Set Parameter Method 9.1 DSP Method 9.2 Convergence of DSP Method 9.3 DSP Elements for Poisson Equation 9.4 DSP Elements for Plate Bending Problem 9.4.1 9-parameter Generalized Conforming Element 9.4.2 VZ1 Element 9.4.3 Variants of VZ1 Element 9.4.4 VZ2 Element 9.4.5 DSPT12 Element 9.4.6 Error Estimate 9.5 A Posteriori Error Estimate Chapter 10 Property of Finite Element Space 10.1 Basic Assumptions 10.2 Embedding Property 10.3 Compact Property 10.4 Inequalities on Finite Element Spaces 10.5 Inequality About Maximum Norm Chapter 11 L_∞ Error Estimate for Second Order Problem 11.1 Weighted Norm 11.2 Regular Green Function 11.3 Conforming Elements 11.4 Nonconforming Elements Chapter 12 L_∞ Error Estimate for Plate Bending Problem 12.1 Regular Green Function 12.2 Conforming Element 12.3 Nonconforming Element 12.4 Quasi-Conforming Element 12.5 Unconventional Element 12.6 DSP Element Bibliography Index
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