Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3972317
- author
- Hansen, Eskil LU and Stillfjord, Tony LU
- organization
- publishing date
- 2013
- 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
- 2024-04-07 14:55:13
@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}}, }