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Produktbild: A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling
Band 136

A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling

Aus der Reihe International Series of Numerical Mathematics

Fr. 138.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.02.2002

Verlag

Springer Basel

Seitenzahl

294

Maße (L/B/H)

24.1/16/2.2 cm

Gewicht

608 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-3-7643-6582-0

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.02.2002

Verlag

Springer Basel

Seitenzahl

294

Maße (L/B/H)

24.1/16/2.2 cm

Gewicht

608 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-3-7643-6582-0

Herstelleradresse

Springer-Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

Email: GPSR Kontakt

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  • Produktbild: A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling
  • 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.- 2.3.1 Front tracking and fixing methods versus fixed domain formulations exemplified by injection and compression moulding.- 2.3.2 Weak formulation.- 2.3.3 The evolutionary variational inequality approach.- 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.- 3.3.1 Time-independent convex sets.- 3.3.2 Time-dependent convex sets.- 3.4 Regularity with respect to space variables.- 3.4.1 Dirichlet boundary conditions.- 3.4.2 Boundary conditions of Neumann/Newton type.- 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.- 4.1.1 The elliptic obstacle problem.- 4.1.2 Finite element approximations for the obstacle problem.- 4.1.3 Basics of finite volume approximations.- 4.1.4 Finite 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.- 4.4.1 Discrete maximum principle.- 4.4.2 Discussion of penalization techniques.- 4.4.3 Iterative solution of the penalization problems.- 4.5 The Signorini problem as a boundary obstacle problem.- 4.6 Results from numerical experiments for elliptic obstacle problems.- 4.6.1 Examples with known exact solution.- 4.6.2 Numerical results for the error between the finite element and the finite volume solution.- 4.6.3 Error behaviour of the finite volume and the penalization solutions.- 5 Numerical Analysis of the Evolutionary Inequalities.- 5.1 Finite element and volume approximations for the evolutionary problems.- 5.1.1 Formulation of the finite element and finite volume approximations.- 5.1.2 Properties of the discrete inequality problems.- 5.1.3 Time evolution of the finite volume solution.- 5.2 Error estimates for the finite element and finite volume solutions.- 5.2.1 Comparison of the finite element and finite volume approximations.- 5.2.2 A priori estimates for the finite element and finite volume solutions.- 5.2.3 Convergence rate for the finite element and finite volume solutions.- 5.3 Penalization methods for the evolutionary finite volume inequalities.- 5.3.1 Discussion of penalization techniques.- 5.3.2 Iterative solution of the penalization problems.- 5.4 Numerical experiments for evolutionary variational inequalities.- 5.4.1 Two evolutionary variational inequalities and the related free boundary problems.- 5.4.2 Numerical results for the errors between exact, finite element and finite volume solution.- 5.4.3 Error behaviour of the penalization solutions.- 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.- 6.2.1 Injection and compression moulding — Technical background and requirements on simulation.- 6.2.1.1 Technical background.- 6.2.1.2 Short comparison of injection/compression moulding and metal casting.- 6.2.1.3 Some aims of the numerical simulation.- 6.2.2 Balance and state equations.- 6.2.3 Rheological behaviour of polymer melts.- 6.2.4 Temperature-dependent Hele-Shaw flow in the injection and compression moulding process.- 6.2.4.1 The generalized Hele-Shaw flow.- 6.2.4.2 Viscosity models and non-isothermal effects.- 6.2.4.3 The numerical core problems.- 6.2.5 The distance concept — a geometrical approach for injection moulding.- 6.2.6 Recent three-dimensional simulation developments.- 6.3 Simulation results.- 6.3.1 Variation of gate location and thickness, non-isothermal effects, narrow flow region.- 6.3.2 Comparison with the distance model.- 6.3.3 Comparison with three-dimensional simulations.- 7 Concluding Remarks.- List of Figures.- List of Tables.- List of Symbols.