Discretizations of nonlinear dissipative evolution equations. Order and convergence.
Author
Summary, in English
For A-stable multistep methods and algebraically stable Runge-Kutta methods the very same global error bounds are obtained in this infinite dimensional setting as derived for stiff ODEs. Error bounds are also presented for full discretizations based on spatial Galerkin approximations.
In contrast to earlier studies, our analysis is not relying on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and a generalization of the classical B-convergence theory.
Department/s
- Mathematics (Faculty of Engineering)
- Numerical Analysis
Publishing year
2005
Language
English
Document type
Dissertation
Publisher
Numerical Analysis, Lund University
Topic
- Mathematics
Keywords
- kontroll
- systems
- numerisk analys
- control
- Datalogi
- numerical analysis
- Computer science
- B-convergence
- Dissipative maps
- Logarithmic Lipschitz constants
- Galerkin methods
- Nonlinear evolution equations
- Time discretizations
- system
Status
Published
Research group
- Numerical Analysis
Supervisor
ISBN/ISSN/Other
- ISBN: 91-628-6668-0
- ISRN: LUTFNA-1001-2005
Defence date
9 December 2005
Defence time
13:15
Defence place
Room MH:C, Centre for Mathematical Sciences, Sölvegatan 18, Lund Institute of Technology
Opponent
- Alexander Ostermann (Professor)