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Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations

Hansen, Eskil LU orcid (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.
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author
organization
publishing date
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
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
2025-10-14 09:02:30
@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}},
}