Jörg Steinbach

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 294
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034875974
• Artikelnr.: 53101951

Inhaltsangabe

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.