Finite element Runge-Kutta discretizations of porous medium type equations
Författare
Summary, in English
In this paper we analyze the convergence properties of full
discretizations of a class of generalized porous medium equations. For the spatial and time discretizations, we use continuous piecewise linear finite elements and algebraically stable Runge-Kutta methods, respectively. We prove our convergence result without any assumption on the spatial regularity. It is shown that, under a certain stability assumption, the temporal order of convergence is given by the stage order of the method, whereas the spatial order is essentially one. Numerical experiments illustrate
our stability assumption and the convergence result.
discretizations of a class of generalized porous medium equations. For the spatial and time discretizations, we use continuous piecewise linear finite elements and algebraically stable Runge-Kutta methods, respectively. We prove our convergence result without any assumption on the spatial regularity. It is shown that, under a certain stability assumption, the temporal order of convergence is given by the stage order of the method, whereas the spatial order is essentially one. Numerical experiments illustrate
our stability assumption and the convergence result.
Avdelning/ar
- Numerical Analysis
- Partial differential equations
Publiceringsår
2008
Språk
Engelska
Sidor
1769-1779
Publikation/Tidskrift/Serie
SIAM Journal on Numerical Analysis
Volym
46
Issue
4
Dokumenttyp
Artikel i tidskrift
Förlag
Society for Industrial and Applied Mathematics
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Nyckelord
- Runge-Kutta time discretization
- high order convergence in time
- degenerate parabolic problems
- porous medium equation
Status
Published
Forskningsgrupp
- Numerical Analysis
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0036-1429