| Issue |
ESAIM: M2AN
Volume 52, Number 6, November-December 2018
|
|
|---|---|---|
| Page(s) | 2307 - 2325 | |
| DOI | https://doi.org/10.1051/m2an/2018040 | |
| Published online | 01 February 2019 | |
Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations
Technical University of Munich, Department of Mathematics, Chair of Optimal Control, Garching, Germany
* Corresponding author: meidner@ma.tum.de
Received:
25
July
2017
Accepted:
22
June
2018
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.
Mathematics Subject Classification: 35K58 / 65M15 / 65M60
Key words: Parabolic semilinear equations / finite elements / Galerkin time discretization / error estimates
© EDP Sciences, SMAI 2019
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