Convergence of MPFA on triangulations and for Richards' equation

By Runhild A. Klausen, Florin Adrian Radu, G. T. Eigestad. 2008

86 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/1a2c6f9b16f8029ef5ec1a23e623fb9ca596fabb

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In Computational Mechanics

In Computational Theory and Mathematics

In Environmental Engineering

Citations in the corpus

A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities (2018, methodology): “In this context we mention Galerkin finite elements [35, 39], MFEM based works [4, 41, 44, 54, 56], multipoint flux approximation (MPFA) [31] or finite volume - MFEM combined methods [21].”
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS (2013, result): “The last goal of the present paper is to, through the preceding developments, show the closeness of mixed finite element methods to various other discretization schemes, namely mimetic finite difference [43, 20, 40], hybrid finite volume [35], mixed finite volume [31], multi-point fluxapproximation ”
A study on iterative methods for solving Richards’ equation (2015, methodology): “…mass conservative schemes for Richards’ equation were proposed and analysed in [Eymard et al.(1999), Eymard et al.(2006)] (finite volumes), in [Klausen et al.(2008)] (multipoint flux approximation) or [Arbogast et al.(1996), Woodward and Dawson(2000), Yotov(1997), Bause and Knabner(2004),…”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, methodology): “They have also been applied to Richards’ equation by a number of researchers (Bergamaschi et al., 1999; Li et al., 2007a; Arrarás et al., 2009; Klausen et al., 2008; Kumar et al., 2009).”
Analysis of an Euler implicit‐mixed finite element scheme for reactive solute transport in porous media (2009, methodology): “As proven in [21], this method can be successfully employed for solving the Richards equation.”