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

Radu AF, Pop IS, Knabner P (2004)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2004

Journal

SIAM Journal on Numerical Analysis Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Book Volume: 42

Pages Range: 1452-1478

Journal Issue: 4

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2004/2004_RaduPopKn_OrderOfConvergenceEstimatesForAnEulerImplicitMixFiniteElementDiscreRichardsEquation

DOI: 10.1137/S0036142902405229

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.

Authors with CRIS profile

Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Eindhoven University of Technology / Technische Universiteit Eindhoven (TU/e) NL Netherlands (NL) University of Bergen / Universitetet i Bergen NO Norway (NO)

How to cite

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: Download