Galerkin time-stepping methods for nonlinear parabolic equations
Computer Science Department, University of Ioannina, 451 10
Ioannina, Greece, email@example.com.
2 Department of Applied Mathematics, University of Crete, 71409 Heraklion-Crete, Greece, and Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion-Crete, Greece, firstname.lastname@example.org.
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.
Mathematics Subject Classification: 65M15 / 65M50
Key words: Nonlinear parabolic equations / local Lipschitz condition / continuous and discontinuous Galerkin methods / a priori error analysis / monotone operators.
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