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Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations

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Author

Summary, in English

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 Delta x(r/2) + Delta t(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. (c) 2006 Elsevier B.V. All rights reserved.

Department/s

Publishing year

2007

Language

English

Pages

882-890

Publication/Series

Journal of Computational and Applied Mathematics

Volume

205

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • logarithmic Lipschitz constants
  • nonlinear parabolic equations
  • Galerkin/Runge-Kutta methods
  • B-convergence

Status

Published

Research group

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0377-0427