Stability of a combined finite element - finite volume discretization of convection-diffusion equations (Q2885151)

The paper is interested in numerical approximation of a time-dependent and a stationary convection-diffusion equation 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. The implicit Euler method is used for the time discretization in the nonstationary case. With an assumption on the underlying mesh, the uniform \(L^{2}\)-stability with respect to the diffusion coefficient is shown. For the time dependent case the stability is furthermore shown to be unconditional.