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First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods

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Abstract

In this paper we show first-order convergence of a multi-point flux approximation control volume method (MPFA) on unstructured triangular grids. In this approach the flux approximation is derived directly in the physical space. In order to do this, we introduce a perturbed mixed finite element method that is equivalent to the MPFA scheme and prove the first-order convergence of this approach. Moreover, we carefully compare the computational performance properties of the MPFA method with those of a lowest order Raviart–Thomas and Brezzi–Douglas–Marini mixed finite element approximation.

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  1. Department Mathematik, Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Markus Bause, Joachim Hoffmann & Peter Knabner

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  1. Markus Bause
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  2. Joachim Hoffmann
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  3. Peter Knabner
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Correspondence to Markus Bause.

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Bause, M., Hoffmann, J. & Knabner, P. First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods. Numer. Math. 116, 1–29 (2010). https://doi.org/10.1007/s00211-010-0290-y

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  • DOI: https://doi.org/10.1007/s00211-010-0290-y

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