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local lipschitz condition

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Galerkin time-stepping methods for nonlinear parabolic equations
Georgios Akrivis, Charalambos Makridakis
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 2 / March 2004

Published online by Cambridge University Press:

15 March 2004, pp. 261-289

Print publication:

March 2004
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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.