Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
Martin Vohralík (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider the lowest-order Raviart–Thomas mixed finite element method for second-order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is...