Galerkin time-stepping methods for nonlinear parabolic equations

We consider discontinuous as well as continuous Galerkin methods for the time discretiza- tion of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity ap riorierror estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation. Mathematics Subject Classification. 65M15, 65M50.

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