Approximations of parabolic variational inequalities

Ženíšek, Alexander. "Approximations of parabolic variational inequalities." Aplikace matematiky 30.1 (1985): 11-35. <http://eudml.org/doc/15382>.

@article{Ženíšek1985,
abstract = {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.},
author = {Ženíšek, Alexander},
journal = {Aplikace matematiky},
keywords = {parabolic variational inequalities; one-step finite difference method; finite element method; convergence; error bound; parabolic variational inequalities; one-step finite difference method; finite element method; convergence; error bound},
language = {eng},
number = {1},
pages = {11-35},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximations of parabolic variational inequalities},
url = {http://eudml.org/doc/15382},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Ženíšek, Alexander
TI - Approximations of parabolic variational inequalities
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 1
SP - 11
EP - 35
AB - 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.
LA - eng
KW - parabolic variational inequalities; one-step finite difference method; finite element method; convergence; error bound; parabolic variational inequalities; one-step finite difference method; finite element method; convergence; error bound
UR - http://eudml.org/doc/15382
ER -