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Dimension splitting for evolution equations

Hansen, Eskil LU and Ostermann, Alexander (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:
author
organization
publishing date
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?
yes
id
2d7b0004-0802-4f9b-8048-0e692645ed00 (old id 936850)
date added to LUP
2008-01-22 19:59:25
date last changed
2017-11-12 03:31:39
@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},
  volume       = {108},
  year         = {2008},
}