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Title: Approximations of parabolic variational inequalities (English)
Author: Ženíšek, Alexander
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 30
Issue: 1
Year: 1985
Pages: 11-35
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form $a(v,w)$ having a potential $J(v)$, which is twice $G$-differentiable at arbitrary $v\in H^1(\Omega)$. This property of $a(v,w)$ makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without any regularity assumptions on the exact solution. An error bound is also derived under the assumption that the exact solution is sufficiently smooth. (English)
Keyword: parabolic variational inequalities
Keyword: one-step finite difference method
Keyword: finite element method
Keyword: convergence
Keyword: error bound
MSC: 49A29
MSC: 49J40
MSC: 65K10
MSC: 65M60
idZBL: Zbl 0574.65066
idMR: MR0779330
DOI: 10.21136/AM.1985.104124
Date available: 2008-05-20T18:26:33Z
Last updated: 2020-07-28
Stable URL:
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