Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Radu AF, Pop IS, Knabner P
Zeitschrift: SIAM Journal on Numerical Analysis
Verlag: Society for Industrial and Applied Mathematics
Jahr der Veröffentlichung: 2004
Band: 42
Heftnummer: 4
Seitenbereich: 1452-1478
ISSN: 0036-1429


Abstract


We analyze a discretization method for a class of degenerate parabolic problems that includes the Richards' equation. This analysis applies to the pressure-based formulation and considers both variably and fully saturated regimes. To overcome the difficulties posed by the lack in regularity, we first apply the Kirchhoff transformation and then integrate the resulting equation in time. We state a conformal and a mixed variational formulation and prove their equivalence. This will be the underlying idea of our technique to get error estimates. A regularization approach is combined with the Euler implicit scheme to achieve the time discretization. Again, equivalence between the two formulations is demonstrated for the semidiscrete case. The lowest order Raviart-Thomas mixed finite elements are employed for the discretization in space. Error estimates are obtained, showing that the scheme is convergent. © 2004 Society for Industrial and Applied Mathematics.


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. (2004). Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation. SIAM Journal on Numerical Analysis, 42(4), 1452-1478. https://dx.doi.org/10.1137/S0036142902405229

MLA:
Radu, Adrian Florin, Iuliu Sorin Pop, and Peter Knabner. "Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation." SIAM Journal on Numerical Analysis 42.4 (2004): 1452-1478.

BibTeX: 

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