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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 },
pages = {261--289},
publisher = {EDP-Sciences},
volume = {38},
number = {2},
year = {2004},
doi = {10.1051/m2an:2004013},
mrnumber = {2069147},
zbl = {1085.65094},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004013/}
}
TY - JOUR AU - Akrivis, Georgios AU - Makridakis, Charalambos TI - Galerkin time-stepping methods for nonlinear parabolic equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 261 EP - 289 VL - 38 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004013/ DO - 10.1051/m2an:2004013 LA - en ID - M2AN_2004__38_2_261_0 ER -
%0 Journal Article %A Akrivis, Georgios %A Makridakis, Charalambos %T Galerkin time-stepping methods for nonlinear parabolic equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2004 %P 261-289 %V 38 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004013/ %R 10.1051/m2an:2004013 %G en %F M2AN_2004__38_2_261_0
Akrivis, Georgios; Makridakis, Charalambos. Galerkin time-stepping methods for nonlinear parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 2, pp. 261-289. doi: 10.1051/m2an:2004013
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