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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.
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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
id
dc3c8ab7-2836-4b83-8858-f3b3274686ba (old id 648809)
date added to LUP
2007-12-11 16:59:24
date last changed
2017-08-06 04:35:31
@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},
  keyword      = {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},
  volume       = {205},
  year         = {2007},
}