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The error structure of the Douglas-Rachford splitting method for stiff linear problems

Hansen, Eskil LU ; Ostermann, Alexander and Schratz, Katharina (2016) In Journal of Computational and Applied Mathematics
Abstract
The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is con- sidered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure. This gives rise to order reductions if the evolution equation does not satisfy extra compatibility assumptions. To remedy the situation one can add correction-terms to the splitting scheme which, e.g., yields the first-order Douglas–Rachford (DR) scheme. In this paper we derive a rigorous error analysis in the setting of linear dissipative operators and inhomo- geneous evolution equations. We also illustrate the order reduction of the Lie splitting, as... (More)
The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is con- sidered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure. This gives rise to order reductions if the evolution equation does not satisfy extra compatibility assumptions. To remedy the situation one can add correction-terms to the splitting scheme which, e.g., yields the first-order Douglas–Rachford (DR) scheme. In this paper we derive a rigorous error analysis in the setting of linear dissipative operators and inhomo- geneous evolution equations. We also illustrate the order reduction of the Lie splitting, as well as the far superior performance of the DR splitting. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Douglas–Rachford splitting, error analysis, order reduction, stiff linear problems, inhomogeneous evolution equations, dissipative operators.
in
Journal of Computational and Applied Mathematics
publisher
Elsevier
external identifiers
  • scopus:84961219103
ISSN
0377-0427
language
English
LU publication?
yes
id
ea7d6c8c-ae27-4dd5-be32-ae485930ff21 (old id 8726267)
date added to LUP
2016-03-11 13:06:27
date last changed
2017-02-13 13:11:24
@article{ea7d6c8c-ae27-4dd5-be32-ae485930ff21,
  abstract     = {The Lie splitting algorithm is frequently used when splitting stiff ODEs or, more generally, dissipative evolution equations. It is unconditionally stable and is con- sidered to be a robust choice of method in most settings. However, it possesses a rather unfavorable local error structure. This gives rise to order reductions if the evolution equation does not satisfy extra compatibility assumptions. To remedy the situation one can add correction-terms to the splitting scheme which, e.g., yields the first-order Douglas–Rachford (DR) scheme. In this paper we derive a rigorous error analysis in the setting of linear dissipative operators and inhomo- geneous evolution equations. We also illustrate the order reduction of the Lie splitting, as well as the far superior performance of the DR splitting.},
  author       = {Hansen, Eskil and Ostermann, Alexander and Schratz, Katharina},
  issn         = {0377-0427},
  keyword      = {Douglas–Rachford splitting,error analysis,order reduction,stiff linear problems,inhomogeneous evolution equations,dissipative operators.},
  language     = {eng},
  month        = {03},
  publisher    = {Elsevier},
  series       = {Journal of Computational and Applied Mathematics},
  title        = {The error structure of the Douglas-Rachford splitting method for stiff linear problems},
  year         = {2016},
}