Buch, Englisch, Band 136, 294 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1340 g
Buch, Englisch, Band 136, 294 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1340 g
Reihe: International Series of Numerical Mathematics
ISBN: 978-3-7643-6582-0
Verlag: Springer
This monograph studies an evolutionary variational inequality approach to a degenerate moving free boundary problem. It takes an intermediate position between elliptic and parabolic inequalities and comprises an elliptic differential operator, a memory term and time-dependent convex constraint sets. Finally, a description of injection and compression moulding is presented in terms of different mathematical models, a generalized Hele-Shaw flow, a distance concept and Navier-Stokes flow.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
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.
