We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.
Mots clés : Parabolic semilinear equations, finite elements, Galerkin time discretization, error estimates
@article{M2AN_2018__52_6_2307_0,
author = {Meidner, Dominik and Vexler, Boris},
title = {Optimal error estimates for fully discrete {Galerkin} approximations of semilinear parabolic equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2307--2325},
publisher = {EDP-Sciences},
volume = {52},
number = {6},
year = {2018},
doi = {10.1051/m2an/2018040},
zbl = {1412.65152},
mrnumber = {3905187},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2018040/}
}
TY - JOUR AU - Meidner, Dominik AU - Vexler, Boris TI - Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 2307 EP - 2325 VL - 52 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2018040/ DO - 10.1051/m2an/2018040 LA - en ID - M2AN_2018__52_6_2307_0 ER -
%0 Journal Article %A Meidner, Dominik %A Vexler, Boris %T Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 2307-2325 %V 52 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2018040/ %R 10.1051/m2an/2018040 %G en %F M2AN_2018__52_6_2307_0
Meidner, Dominik; Vexler, Boris. Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2307-2325. doi : 10.1051/m2an/2018040. http://archive.numdam.org/articles/10.1051/m2an/2018040/
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