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Franz-Theo Suttmeier
Numerical solution of Variational Inequalities by Adaptive Finite Elements
erschienen August 2008
161 Seiten, 41 schw.-w. u. 10 farb. Abb., 24 schw.-w. Tab., Paperback
Vieweg+Teubner Verlag | ISBN: 3834806641
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| KLAPPENTEXT | öffnen |
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Numerical Solution of Variational Inequalities by Adaptive Finite Elements Franz-Theo Suttmeier describes a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the Solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a p... [weiter lesen] |
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| AUTOR | öffnen |
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About the Author Dr. Franz-Theo Suttmeier is a professor of Scientific Computing at the Institute of Applied Analysis and Numerics at the University of Siegen. [weiter lesen] |
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| INHALTSVERZEICHNIS | öffnen |
Contents
1 Introduction 1
2 Models in elasto-plasticity 13
2.1 Governing equations 14
2.2 Examples 20
3 The dual-weighted-residual method 23
3.1 A model Situation in plasticity 24
3.2 A posteriori error estimate 25
3.3 Evaluation of a posteriori error bounds 26
3.4 Strategies for mesh adaptation 28
3.5 Example 30
4 Extensions to stabilised schemes 33
4.1 Discretisation for the membrane-problem 35
4.2 A posteriori error analysis 37
4.3 Numerical tests 42
5 Obstacle problem 47
5.1 Energy norm 48
5.2 Duality argument 49
5.3 A posteriori estimates 51
5.4 Numerical results 54
6 Signorini's problem 57
6.1 A posteriori error bounds 58
6.2 Numerical results 62
6.3 A posteriori controlled boundary approximation 66
7 Strang's problem 69
7.1 A posteriori error bounds 70
7.2 Numerical results 73
8 General concept 75
8.1 Orthogonality relation 75
8.2 Duality argument 76
8.3 Modifikation 77
8.3.1 Example 79
9 Lagrangian formalism 81
9.1 Torsion problem 81
9.2 A suboptimal error estimate 83
9.3 Saddle point problem 84
9.3.1 Discretisation error of the Lagrange multiplier 86
9.3.2 Discretisation error of the primal variable 87
10 Obstacle problem revisited 91
10.1 Weak formulation 91
10.2 A posteriori error estimates 92
10.3 Numerical results 94
11 Variational inequalities of second kind 95
11.1 A flow problem 95
11.1.1 Saddle point problem 96
11.2 A friction problem 97
11.2.1 Saddle point problem 98
11.3 A posteriori error estimate 99
11.4 Numerical results 101
11.4.1 Bingham fluid 101
11.4.2 Friction problem 102
12 Time-dependent problems 105
12.1 Discretisation 105
12.2 Error estimation 107
13 Applications 109
13.1 Grinding 109
13.1.1 Discretisation 110
13.1.2 Solution Process 111
13.1.3 Simulation 112
13.2 Milling 116
13.3 Elasto-plastic benchmark problem 117
13.3.1 Solution of the benchmark: Hencky model 120
13.3.2 Solution of the benchmark: Prandtl-Reuss model 126
14 Iterative Algorithms 129
14.1 Introduction 129
14.2 A Smoothing Procedure 131
14.3 The Multilevel Procedure 132
14.4 A Conjugate Gradient Algorithm 134
14.5 Numerical Results 135
14.5.1 Example 1135
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