Error estimates for a mixed finite element discretization of some degenerate parabolic equations

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Radu AF, Pop IS, Knabner P
Zeitschrift: Numerische Mathematik
Verlag: Springer Verlag (Germany)
Jahr der Veröffentlichung: 2008
Band: 109
Heftnummer: 2
Seitenbereich: 285-311
ISSN: 0029-599X


Abstract


We consider a numerical scheme for a class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards equation modeling the flow in porous media. The numerical scheme is based on the mixed finite element method (MFEM) in space, and is of one step implicit in time. The lowest order Raviart-Thomas elements are used. Here we extend the results in Radu et al. (SIAM J Numer Anal 42:1452-1478, 2004), Schneid et al. (Numer Math 98:353-370, 2004) to a more general framework, by allowing for both types of degeneracies. We derive error estimates in terms of the discretization parameters and show the convergence of the scheme. The features of the MFEM, especially of the lowest order Raviart-Thomas elements, are now fully exploited in the proof of the convergence. The paper is concluded by numerical examples. © 2008 Springer-Verlag.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Einrichtungen weiterer Autorinnen und Autoren

Eindhoven University of Technology / Technische Universiteit Eindhoven (TU/e)
University of Bergen / Universitetet i Bergen


Zitierweisen

APA:
Radu, A.F., Pop, I.S., & Knabner, P. (2008). Error estimates for a mixed finite element discretization of some degenerate parabolic equations. Numerische Mathematik, 109(2), 285-311. https://dx.doi.org/10.1007/s00211-008-0139-9

MLA:
Radu, Adrian Florin, Iuliu Sorin Pop, and Peter Knabner. "Error estimates for a mixed finite element discretization of some degenerate parabolic equations." Numerische Mathematik 109.2 (2008): 285-311.

BibTeX: 

Zuletzt aktualisiert 2019-10-07 um 12:12