no. 2
Galerkin time-stepping methods for nonlinear parabolic equations
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 261-289.

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.

DOI : 10.1051/m2an:2004013
Classification : 65M15, 65M50
Mots clés : nonlinear parabolic equations, local Lipschitz condition, continuous and discontinuous Galerkin methods, a priori error analysis, monotone operators 
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     title = {Galerkin time-stepping methods for nonlinear parabolic equations},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {261--289},
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Akrivis, Georgios; Makridakis, Charalambos. Galerkin time-stepping methods for nonlinear parabolic equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 2, pp. 261-289. doi : 10.1051/m2an:2004013. http://www.numdam.org/articles/10.1051/m2an:2004013/

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