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Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations

Hansen, Eskil LU and Stillfjord, Tony LU orcid (2013) In Mathematics of Computation 82(284). p.1975-1985
Abstract
We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler schemes have the same convergence order, i.e., between one half and one depending on the initial values and the vector fields. Concrete applications include the discretization of diffusion-reaction systems, with fully nonlinear and degenerate diffusion terms. The convergence and efficiency of the IMEX Euler scheme are also illustrated by a set of numerical... (More)
We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler schemes have the same convergence order, i.e., between one half and one depending on the initial values and the vector fields. Concrete applications include the discretization of diffusion-reaction systems, with fully nonlinear and degenerate diffusion terms. The convergence and efficiency of the IMEX Euler scheme are also illustrated by a set of numerical experiments. (Less)
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Implicit-explicit Euler scheme, convergence orders, nonlinear evolution equations, dissipative operators
in
Mathematics of Computation
volume
82
issue
284
pages
1975 - 1985
publisher
American Mathematical Society (AMS)
external identifiers
  • wos:000326291500005
  • scopus:84880656692
ISSN
1088-6842
DOI
10.1090/S0025-5718-2013-02702-0
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
6d4c923b-dd47-451b-9f4c-6a15c4367205 (old id 3972317)
alternative location
http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02702-0/
date added to LUP
2016-04-01 10:42:12
date last changed
2022-04-04 20:33:29
@article{6d4c923b-dd47-451b-9f4c-6a15c4367205,
  abstract     = {{We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler schemes have the same convergence order, i.e., between one half and one depending on the initial values and the vector fields. Concrete applications include the discretization of diffusion-reaction systems, with fully nonlinear and degenerate diffusion terms. The convergence and efficiency of the IMEX Euler scheme are also illustrated by a set of numerical experiments.}},
  author       = {{Hansen, Eskil and Stillfjord, Tony}},
  issn         = {{1088-6842}},
  keywords     = {{Implicit-explicit Euler scheme; convergence orders; nonlinear evolution equations; dissipative operators}},
  language     = {{eng}},
  number       = {{284}},
  pages        = {{1975--1985}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Mathematics of Computation}},
  title        = {{Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations}},
  url          = {{https://lup.lub.lu.se/search/files/2066306/3972332.pdf}},
  doi          = {{10.1090/S0025-5718-2013-02702-0}},
  volume       = {{82}},
  year         = {{2013}},
}