Evaluation de l'erreur d'approximation pour une in�quation parabolique relative aux convexes d�pendant du temps

Abstract

R6sum6. On commence en posant un probl6me d'6volution avec contraintes unilat6rales, d6pendantes du temps, pour lequel on donne deux th6or~mes de r6gularit6.On fait ensuite l'approximation num6rique par la m6thode des 616ments finis et on montre un algorithme de r6solution pour les syst6mes de compl6mentarit6 associ6s aux probl~mes approch6s.On obtient enfin une majoration de l'erreur d'approximation.

The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis

“…Error bounds for parabolic variational inequalities have been calculated by Johnson (1976), Berger & Falk (1977), Scarpini & Vivaldi (1978), Colli & Verdi (1985), Fetter (1987) and Vuik (1990). In each they essentially consider the same Dirichlet problem but with a varying obstacle constraint.…”

“…In Johnson (1976), Berger & Falk (1977), Fetter (1987) and Vuik (1990) they have a fixed single obstacle. In Colli & Verdi (1985) the obstacle constraint is only applied on part of dQ, and in Scarpini & Vivaldi (1978) the double obstacle is time dependent.…”

AnL 2-error estimate for an approximation of the solution of a parabolic variational inequality

“…As far as earlier work in this area is concerned we note that: in [11 ] and [13] an if-error estimate is given by using a backward difference in time. Reference [1] give an L2-error estimate using a forward difference in time and lumping of the mass matrix.…”