Geodesic
Approximations of parabolic variational inequalities
Applications of Mathematics, Tome 30 (1985) no. 1, pp. 11-35.

Voir la notice de l'article dans Czech Digital Mathematics Library

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∈H1(Ω). 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.
DOI : 10.21136/AM.1985.104124
Classification : 49A29, 49J40, 65K10, 65M60
Mots-clés : parabolic variational inequalities; one-step finite difference method; finite element method; convergence; error bound 
@article{10_21136_AM_1985_104124,
     author = {\v{Z}en{\'\i}\v{s}ek, Alexander},
     title = {Approximations of parabolic variational inequalities},
     journal = {Applications of Mathematics},
     pages = {11--35},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {1985},
     doi = {10.21136/AM.1985.104124},
     mrnumber = {0779330},
     zbl = {0574.65066},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104124/}
}
TY  - JOUR
AU  - Ženíšek, Alexander
TI  - Approximations of parabolic variational inequalities
JO  - Applications of Mathematics
PY  - 1985
SP  - 11
EP  - 35
VL  - 30
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104124/
DO  - 10.21136/AM.1985.104124
LA  - en
ID  - 10_21136_AM_1985_104124
ER  - 
%0 Journal Article
%A Ženíšek, Alexander
%T Approximations of parabolic variational inequalities
%J Applications of Mathematics
%D 1985
%P 11-35
%V 30
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104124/
%R 10.21136/AM.1985.104124
%G en
%F 10_21136_AM_1985_104124
Ženíšek, Alexander. Approximations of parabolic variational inequalities. Applications of Mathematics, Tome 30 (1985) no. 1, pp. 11-35. doi : 10.21136/AM.1985.104124. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104124/

Cité par Sources :