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Galerkin time-stepping methods for nonlinear parabolic equations. (English) Zbl 1085.65094
The paper describes a priori analysis of variational time discretization methods for nonlinear parabolic partial differential equations using either the discontinuous or the continuous Galerkin method. Existence and local uniqueness of the Galerkin approximations are shown for a modified equation with globally Lipschitz continuous nonlinearity and optimal order a priori error estimates are derived using an abstract Hilbert space setting. Fully discretized equations are also considered, applying Galerkin discretizations in space-time. Finally, the results are illustrated for a quasilinear parabolic equation.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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