Equivalence between mixed finite element and multi-point finite volume methods. (English) Zbl 1058.65132
Summary: We consider the lowest-order Raviart-Thomas mixed finite element method for elliptic problems on simplicial meshes in two or three space dimensions. This method produces saddle-point type problems for scalar and flux unknowns. We show how to easily eliminate the flux unknowns, which implies an equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. We describe the stencil of the final matrix and give sufficient conditions for its symmetry and positive definiteness. We present a numerical example illustrating the performance of the proposed method.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
Keywords:
Raviart-Thomas mixed finite element method; simplicial meshes; saddle-point type problems; multi-point finite volume scheme; numerical exampleReferences:
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