Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations
Hansen, Eskil LU
(2007)
In Journal of Computational and Applied Mathematics
205(2).
p.882-890
- 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 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.
Please use this url to cite or link to this publication:
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- author
- Hansen, Eskil
LU
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- logarithmic Lipschitz constants, nonlinear parabolic equations, Galerkin/Runge-Kutta methods, B-convergence
- in
- Journal of Computational and Applied Mathematics
- volume
- 205
- issue
- 2
- pages
- 882 - 890
- publisher
- Elsevier
- external identifiers
-
- wos:000247261300020
- scopus:34248201578
- ISSN
- 0377-0427
- DOI
- 10.1016/j.cam.2006.03.041
- project
- Numerical Analysis and Scientific Computing
- Partial Differential Equations
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- dc3c8ab7-2836-4b83-8858-f3b3274686ba (old id 648809)
- date added to LUP
- 2016-04-01 16:34:28
- date last changed
- 2026-02-11 13:53:28
@article{dc3c8ab7-2836-4b83-8858-f3b3274686ba,
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 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.}},
author = {{Hansen, Eskil}},
issn = {{0377-0427}},
keywords = {{logarithmic Lipschitz constants; nonlinear parabolic equations; Galerkin/Runge-Kutta methods; B-convergence}},
language = {{eng}},
number = {{2}},
pages = {{882--890}},
publisher = {{Elsevier}},
series = {{Journal of Computational and Applied Mathematics}},
title = {{Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations}},
url = {{http://dx.doi.org/10.1016/j.cam.2006.03.041}},
doi = {{10.1016/j.cam.2006.03.041}},
volume = {{205}},
year = {{2007}},
}