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Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations

2018; EDP Sciences; Volume: 52; Issue: 6 Linguagem: Inglês

10.1051/m2an/2018040

1290-3841

Dominik Meidner, Boris Vexler,

Advanced Numerical Methods in Computational Mathematics

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.