| Title | Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations |
| Authors | Eskil Hansen |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Computational and Applied Mathematics |
| Year | 2007 |
| Volume | 205 |
| Issue | 2 |
| Pages | 882 - 890 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier |
| Abstract 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. |
| Keywords | logarithmic Lipschitz constants, nonlinear parabolic equations, Galerkin/Runge-Kutta methods, B-convergence, |
| ISBN/ISSN/Other | ISSN: 0377-0427 |
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