We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
@article{M2AN_2004__38_2_261_0,
author = {Akrivis, Georgios and Makridakis, Charalambos},
title = {Galerkin time-stepping methods for nonlinear parabolic equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {38},
year = {2004},
pages = {261-289},
doi = {10.1051/m2an:2004013},
mrnumber = {2069147},
zbl = {1085.65094},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2004__38_2_261_0}
}
Akrivis, Georgios; Makridakis, Charalambos. Galerkin time-stepping methods for nonlinear parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 261-289. doi : 10.1051/m2an:2004013. http://gdmltest.u-ga.fr/item/M2AN_2004__38_2_261_0/
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