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Galerkin time-stepping methods for nonlinear parabolic equations

Published online by Cambridge University Press:  15 March 2004

Georgios Akrivis  and
Charalambos Makridakis
Georgios Akrivis
Affiliation:
Computer Science Department, University of Ioannina, 451 10 Ioannina, Greece, [email protected].
Charalambos Makridakis
Affiliation:
Department of Applied Mathematics, University of Crete, 71409 Heraklion-Crete, Greece, and Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion-Crete, Greece, [email protected].
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Abstract

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.

Keywords

Nonlinear parabolic equationslocal Lipschitz conditioncontinuous and discontinuous Galerkin methodsa priori error analysismonotone operators.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 261 - 289
Copyright
© EDP Sciences, SMAI, 2004

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References

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