Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. (English) Zbl 1116.65121

Vohralík, Martin

ESAIM, Math. Model. Numer. Anal. 40, No. 2, 367-391 (2006).

The paper is concerned with the lowest order Raviart-Thomas element for elliptic problems of second order on simplicial meshes in \(2\)-D or \(3\)-D. An elimination of the fluxes is performed. It shows the equivalence to a finite volume method. In contrast to the implementation by D. N. Arnold and F. Brezzi [RAIRO, Modélisation Math. Anal. Numer. 19, 7–32 (1985; Zbl 0567.65078)] the resulting matrix is in general unsymmetric. The extension to nonlinear parabolic convection-diffusion equations is shown. The paper concludes with several numerical examples.

Reviewer: Dietrich Braess (Bochum)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations

Keywords:

mixed methods; finite volume method; Raviart-Thomas element; elliptic problems of second order; nonlinear parabolic convection-diffusion equations; numerical examples

Citations:

Zbl 0567.65078

Software:

symrcm

References:

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