Abstract
This paper is devoted to the numerical solution of variational inequalities, which are used to simulate the injection moulding process of a plastic melt into a mould cavity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Austin, C., White, J.W., Filling of mold cavities, the injection molding process, in “Computer aided engineering for injection molding,” (ed. Bernhardt E.C.) Carl Hanser Verlag, München, 1983.
Bensoussan, A, Lions, J.L., “Applications of variational inequalities in stochastic control,” North-Holland Publishing Company, Amsterdam, 1982.
Bensoussan, A., Lions, J.L., “Contrôle impulsionnel et inéquations quasivariationnelles,” Dunod—Bordas, Paris, 1982.
Brezzi, F., Hager, W.W., Raviart, P.A., Error estimates for the finite element solution of variational inequalities, Part I—Primal theory, Numer. Math. 28 (1977), 431–443.
Gajewski, H., Gröger, K., Zacharias, K., “Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen,” Akademie — Verlag, Berlin, 1974.
Glowinski, R., “Numerical methods for nonlinear variational problems,” Tata institute of fundamental research, Bombay, Springer-Verlag, 1980.
Glowinski, R., Lions, J.L., Tremolieres, R., “Analyse numérique des inéquations variationelles,” Dunod-Bordas, Paris, 1976.
Hartwig, K.H., Weinelt, W., Numerische Lösung linearer elliptischer Variationsungleichungen mittels FDM, WSR der TH K. —M. —St. 8 (1985).
Kacur, J., “Method of Rothe in evolution equations,” Teubner — Text 80, Leipzig, 1985.
Kinderlehrer, D., Stampacchia, G., “An introduction to variational inequalities and their applications,” Academic Press, New York, 1980.
Lions, J., “Quelques méthodes de résolution des problèmes aux limites non linéaires (Russian),” Dunod, Gauthier-Villars, Paris, 1969.
Scholz, R., Numerical solution of the obstacle problem by the penalty method, Computing 32 (1984), 297–306.
Steinbach, J., Existenzsätze für eine Klasse von evolutionären Variationsungleichungen, WZ der TU K. —M. —St. 30 1 (1988), 22–26.
Steinbach, J., Untersuchungen zu evolutionären Variationsungleichungen, WZ der TU K. —M. —St. 31 2 (1989), 257–262.
Steinbach, J., “Numerische Lösung elliptischer und evolutionärer Variationsungleichungen mittels Differenzenverfahren,” Thesis TU K. —M. —St., 1990.
Weinelt, W., Hartwig, K.H., Zur mathematischen Modellierung von Spritzgießprozessen, WZ der TU K. —M. —St. 28 2 (1986), 153–160.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Basel AG
About this chapter
Cite this chapter
Steinbach, J. (1991). FDM approximation of variational inequalities with an application to injection moulding. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_35
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5715-4_35
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5717-8
Online ISBN: 978-3-0348-5715-4
eBook Packages: Springer Book Archive