Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations
(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:
https://lup.lub.lu.se/record/648809
- 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
- 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
- 2020-12-08 03:44:11
@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}, 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}, }