DeutschesFachbuch.de : Numerical solution of Variational Inequalities by Adaptive Finite Elements Von Franz-Theo Suttmeier

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 1	135
		14.5.2	Example 2	138

15	Conclusion			141
A Algorithmic Aspects				143
Bibliography				155