Geodesic
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

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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.

DOI : 10.1051/m2an/2018040
Classification : 35K58, 65M15, 65M60
Keywords: Parabolic semilinear equations, finite elements, Galerkin time discretization, error estimates

Meidner, Dominik 1 ; Vexler, Boris 1

1 
@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://geodesic.mathdoc.fr/articles/10.1051/m2an/2018040/}
}
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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

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