Author | Steinbach, Jรถrg. author |
---|---|
Title | A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling [electronic resource] / by Jรถrg Steinbach |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7597-4 |
Descript | X, 294 p. online resource |
1 Introduction -- 2 Evolutionary Variational Inequality Approach -- 2.1 The degenerate free boundary problem -- 2.2 Some application problems -- 2.3 Different fixed domain formulations -- 3 Properties of the Variational Inequality Solution -- 3.1 Problem setting and general notations -- 3.2 Existence and uniqueness result -- 3.3 Monotonicity properties and regularity with respect to time -- 3.4 Regularity with respect to space variables -- 3.5 Some remarks on further regularity results -- 4 Finite Volume Approximations for Elliptic Inequalities -- 4.1 Finite element and volume approximations for the obstacle problem -- 4.2 Comparison of finite volume and finite element approximations -- 4.3 Error estimates for the finite volume solution -- 4.4 Penalization methods for the finite volume obstacle problem -- 4.5 The Signorini problem as a boundary obstacle problem -- 4.6 Results from numerical experiments for elliptic obstacle problems -- 5 Numerical Analysis of the Evolutionary Inequalities -- 5.1 Finite element and volume approximations for the evolutionary problems -- 5.2 Error estimates for the finite element and finite volume solutions -- 5.3 Penalization methods for the evolutionary finite volume inequalities -- 5.4 Numerical experiments for evolutionary variational inequalities -- 6 Injection and Compression Moulding as Application Problems -- 6.1 Classical Hele-Shaw flows and related moving boundary problems -- 6.2 Mathematical modelling of injection and compression moulding -- 6.3 Simulation results -- 7 Concluding Remarks -- List of Figures -- List of Tables -- List of Symbols