First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods
The authors show first order convergence of a multi-point flux approximation (MPFA) control volume method on an unstructured triangular grid. A perturbed mixed finite element method with broken Raviart-Thomas elements and a specific quadrature rule is introduced and the equivalence of the MPFA method with a hybrid variant of the mixed method is proved. The theoretical error estimates are verified by numerical convergence studies. The accuracy of the MPFA approximation is carefully compared with that of a lowest order Raviart-Thomas and Brezzi-Douglas-Marini approach.
multi-point flux approximation control volume methods
scientific article; zbMATH DE number 5764625
scientific article