Numerical Solutions of PDEs by the Finite Element Method - Johnson.djvu: Numerical_Solutions_of_PDEs_by_the_Finite_Element_Method_-_Johnson.djvu

Preface 7
0. Introduction 9
0.1 Background 9
0.2 Difference methods- Finite element methods
0.3 Scope of the book 12
10
1. Introduction to FEM for elliptic problems 14
1ol Variational formulation of a one-dimensional model problem
1o2 FEM for the model problem with piecewise linear functions
1.3 An error estimate for FEM for the model problem 23
1.4 FEM for the Poisson equation 26
1.5 The Hilbert spaces L:(f2), Hi(f2) and H(f2) 33
1.6 A geometric interpretation of FEM 38
1.7 A Neumann problem. Natural and essential boundary conditions
1.8 Remarks on programming 43
1.9 Remarks on finite element software 48
14
18
2. Abstract formulation of the finite element method for elliptic problems
2.1 Introduction. The continuous problem 50
2.2 Discretization. An error estimate 52
2.3 The energy norm 55
2.4 Some examples 55
3. Some finite element spaces 67
3.1 Introduction. Regularity requirements
3.2 Some examples of finite elements 68
3.3 Summary 79
67
4. Approximation theory for FEM. Error estimates for elliptic problems
4.1 Introduction 84
4.2 Interpolation with piecewise linear functions in two dimensions 84

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