Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations

Authors:
Eskil Hansen
Affiliations:
Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

Global error bounds are derived for full Galerkin/Runge-Kutta discretizations of nonlinear parabolic problems, including the evolution governed by the p-Laplacian with p=2. The analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and an extended B-convergence theory. The global error is bounded in L"2 by @Dx^r^/^2+@Dt^q, where r is the convergence order of the Galerkin method applied to the underlying stationary problem and q is the stiff order of the algebraically stable Runge-Kutta method.