Unconditional convergence of DIRK schemes applied to dissipative evolution equations
Author
Summary, in English
In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, which enables the usage of an abstract approximation result for dissipative maps. The analysis is also extended to the case where the dissipative vector field is perturbed by a locally Lipschitz continuous map. The efficiency and robustness of these schemes are finally illustrated by applying them to a nonlinear diffusion equation.
Department/s
- Mathematics (Faculty of Engineering)
- Partial differential equations
- Numerical Analysis
Publishing year
2010
Language
English
Pages
55-63
Publication/Series
Applied Numerical Mathematics
Volume
60
Issue
1-2
Document type
Journal article
Publisher
Elsevier
Topic
- Mathematics
Keywords
- Dissipative evolution equations
- DIRK schemes
- Convergence
- Nonlinear parabolic problems
Status
Published
Research group
- Partial differential equations
- Numerical Analysis
ISBN/ISSN/Other
- ISSN: 0168-9274