Decentrage et elements finis mixtes pour les équations de diffusion- convection. (French) Zbl 0562.65077

The diffusion-convection equation in two spatial dimensions is approximated by mixed finite elements using an unsymmetric approach (due to Lesaint/Raviart) for the convection term: For a dissipation parameter \(0\leq \delta \leq 1\), one gets a centered scheme in case \(\delta =0\) and an upwind scheme if \(\delta =1\). (Besides this, there is no indication how to choice that parameter in a practical problem, say in dependence on coefficients and triangulation.) Existence, uniqueness and error estimates are proven in the elliptic and (for the semi-discrete approximation) in the parabolic case, including estimates for diffusion tending to zero.
Reviewer: G.Stoyan


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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