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Finite element Runge-Kutta discretizations of porous medium type equations
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- Hansen, Eskil (author)
- Lund University,Lunds universitet,Numerisk analys,Forskargrupper vid Lunds universitet,Partiella differentialekvationer,Numerical Analysis,Lund University Research Groups,Partial differential equations,University of Innsbruck
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- Ostermann, Alexander (author)
- University of Innsbruck
- (creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2008
- 2008
- English.
- In: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 46:4, s. 1769-1779
- Journal article (peer-reviewed)
Abstract
Subject headings
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- 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.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)
Keyword
- Runge-Kutta time discretization
- high order convergence in time
- degenerate parabolic problems
- porous medium equation
Publication and Content Type
- art (subject category)
- ref (subject category)
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