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Finite element Runge-Kutta discretizations of porous medium type equations

Hansen, Eskil LU orcid and Ostermann, Alexander (2008) In SIAM Journal on Numerical Analysis 46(4). p.1769-1779
Abstract
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.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Runge-Kutta time discretization, high order convergence in time, degenerate parabolic problems, porous medium equation
in
SIAM Journal on Numerical Analysis
volume
46
issue
4
pages
1769 - 1779
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:55349091064
ISSN
0036-1429
DOI
10.1137/070680953
language
English
LU publication?
yes
id
c0aed93e-6b34-4b40-9f29-87b90e56909a (old id 936962)
date added to LUP
2016-04-01 14:21:34
date last changed
2024-01-25 15:13:49
@article{c0aed93e-6b34-4b40-9f29-87b90e56909a,
  abstract     = {{In this paper we analyze the convergence properties of full<br/><br>
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<br/><br>
our stability assumption and the convergence result.}},
  author       = {{Hansen, Eskil and Ostermann, Alexander}},
  issn         = {{0036-1429}},
  keywords     = {{Runge-Kutta time discretization; high order convergence in time; degenerate parabolic problems; porous medium equation}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1769--1779}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Numerical Analysis}},
  title        = {{Finite element Runge-Kutta discretizations of porous medium type equations}},
  url          = {{http://dx.doi.org/10.1137/070680953}},
  doi          = {{10.1137/070680953}},
  volume       = {{46}},
  year         = {{2008}},
}