Hybrid and multi-point formulations of the lowest-order mixed methods for Darcy's flow on triangles

Anis Younes (1) , Vincent Fontaine (2)

1 IMFS - Institut de Mécanique des Fluides et des Solides
2 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

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. x-audience © 2008 John Wiley & Sons, Ltd.

Mots clés: Brezzi-Douglas-Marini space; hybrid formulation; mixed method; multipoint flux approximation; Raviart-Thomas space

Domaines: Sciences de l'ingénieur [physics]

Anis Younes, Vincent Fontaine. Hybrid and multi-point formulations of the lowest-order mixed methods for Darcy's flow on triangles. International Journal for Numerical Methods in Fluids, 2008, 58 (9), pp.1041-1062. ⟨10.1002/fld.1785⟩. ⟨hal-00919722⟩