Dimension splitting for quasilinear parabolic equations
(2010) In IMA Journal of Numerical Analysis 30(3). p.857-869- Abstract
- In the current paper, we derive a rigorous convergence analysis for
a broad range of splitting schemes applied to abstract nonlinear
evolution equations, including the Lie and Peaceman-Rachford
splittings. The analysis is in particular applicable to (possibly
degenerate) quasilinear parabolic problems and their dimension
splittings. The abstract framework is based on the theory of maximal
dissipative operators, and we both give a summary of the used theory
and some extensions of the classical results. The derived
convergence results are illustrated by numerical experiments.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/936936
- author
- Hansen, Eskil LU and Ostermann, Alexander
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- degeneracy, quasilinear parabolic problems, convergence, dimension splitting
- in
- IMA Journal of Numerical Analysis
- volume
- 30
- issue
- 3
- pages
- 857 - 869
- publisher
- Oxford University Press
- external identifiers
-
- scopus:77956017644
- ISSN
- 0272-4979
- DOI
- 10.1093/imanum/drn078
- language
- English
- LU publication?
- no
- id
- ec81b351-ef4d-47d5-bfe0-3ffba818a541 (old id 936936)
- date added to LUP
- 2016-04-01 10:24:24
- date last changed
- 2024-08-12 21:39:59
@article{ec81b351-ef4d-47d5-bfe0-3ffba818a541, abstract = {{In the current paper, we derive a rigorous convergence analysis for<br/><br> a broad range of splitting schemes applied to abstract nonlinear<br/><br> evolution equations, including the Lie and Peaceman-Rachford<br/><br> splittings. The analysis is in particular applicable to (possibly<br/><br> degenerate) quasilinear parabolic problems and their dimension<br/><br> splittings. The abstract framework is based on the theory of maximal<br/><br> dissipative operators, and we both give a summary of the used theory<br/><br> and some extensions of the classical results. The derived<br/><br> convergence results are illustrated by numerical experiments.}}, author = {{Hansen, Eskil and Ostermann, Alexander}}, issn = {{0272-4979}}, keywords = {{degeneracy; quasilinear parabolic problems; convergence; dimension splitting}}, language = {{eng}}, number = {{3}}, pages = {{857--869}}, publisher = {{Oxford University Press}}, series = {{IMA Journal of Numerical Analysis}}, title = {{Dimension splitting for quasilinear parabolic equations}}, url = {{http://dx.doi.org/10.1093/imanum/drn078}}, doi = {{10.1093/imanum/drn078}}, volume = {{30}}, year = {{2010}}, }