Dimension splitting for evolution equations
(2008) In Numerische Mathematik 108(4). p.557-570- Abstract
- In this paper, we are concerned with splitting methods for the time integration of abstract evolution equations. We introduce an analytic framework which allows us to prove optimal convergence orders for various splitting methods, including the Lie and Peaceman–Rachford splittings. Our setting is applicable for a wide variety of linear equations and their dimension splittings. In particular, we analyze parabolic problems with Dirichlet boundary conditions, as well as degenerate equations on bounded domains. We further illustrate our theoretical results with a set of numerical experiments.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/936850
- author
- Hansen, Eskil LU and Ostermann, Alexander
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Numerische Mathematik
- volume
- 108
- issue
- 4
- pages
- 557 - 570
- publisher
- Springer
- external identifiers
-
- scopus:38549117840
- ISSN
- 0029-599X
- DOI
- 10.1007/s00211-007-0129-3
- language
- English
- LU publication?
- no
- id
- 2d7b0004-0802-4f9b-8048-0e692645ed00 (old id 936850)
- date added to LUP
- 2016-04-01 12:32:02
- date last changed
- 2024-08-15 05:56:14
@article{2d7b0004-0802-4f9b-8048-0e692645ed00, abstract = {{In this paper, we are concerned with splitting methods for the time integration of abstract evolution equations. We introduce an analytic framework which allows us to prove optimal convergence orders for various splitting methods, including the Lie and Peaceman–Rachford splittings. Our setting is applicable for a wide variety of linear equations and their dimension splittings. In particular, we analyze parabolic problems with Dirichlet boundary conditions, as well as degenerate equations on bounded domains. We further illustrate our theoretical results with a set of numerical experiments.}}, author = {{Hansen, Eskil and Ostermann, Alexander}}, issn = {{0029-599X}}, language = {{eng}}, number = {{4}}, pages = {{557--570}}, publisher = {{Springer}}, series = {{Numerische Mathematik}}, title = {{Dimension splitting for evolution equations}}, url = {{http://dx.doi.org/10.1007/s00211-007-0129-3}}, doi = {{10.1007/s00211-007-0129-3}}, volume = {{108}}, year = {{2008}}, }