We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element-finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is shown to be unconditionally L 2-stable, uniformly with respect to the diffusion coefficient.
We consider a time-dependent and a stationary convection-diffusion equation. These equations are approximated by a combined finite element -finite volume method: the diffusion term is discretized by CrouzeixRaviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the nonstationary case, we use an implicit Euler approach for time discretization. This scheme is shown to be L 2 -stable uniformly with respect to the diffusion coefficient. In addition, it turns out that stability is unconditional in the time-dependent case. These results hold if the underlying grid satisfies a condition that is fulfilled, for example, by some structured meshes.
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