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Hybrid and multi‐point formulations of the lowest‐order mixed methods for Darcy's flow on triangles
Author(s) -
Younes Anis,
Fontaine Vincent
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1785
Subject(s) - polygon mesh , anisotropy , flow (mathematics) , finite element method , point (geometry) , mathematics , computer science , mathematical optimization , geometry , physics , thermodynamics , quantum mechanics
Abstract Mixed finite element (MFE) and multipoint flux approximation (MPFA) methods have similar properties and are well suited for the resolution of Darcy's flow on anisotropic and heterogeneous domains. In this work, the link between hybrid and MPFA formulations is shown algebraically for the lowest order mixed methods of Raviart–Thomas (RT0) and Brezzi–Douglas–Marini (BDM1) on triangles. The efficiency of the four mixed formulations (Hybrid_RT0, MPFA_RT0, Hybrid_BDM1 and MPFA_BDM1) is investigated on high anisotropic and heterogeneous media and for unstructured triangular discretizations. Numerical experiments show that the MPFA_BDM1 formulation outperforms both Hybrid_RT0 and Hybrid_BDM1 in the case of anisotropic domains and highly unstructured meshes. Copyright © 2008 John Wiley & Sons, Ltd.