Error estimates for a finite element-finite volume discretization of convection-diffusion equations

Authors:
Paul Deuring;Marcus Mildner
Affiliations:
Univ Lille Nord de France, F-59000 Lille, France and ULCO, LMPA, F-62228 Calais, France;Univ Lille Nord de France, F-59000 Lille, France and ULCO, LMPA, F-62228 Calais, France
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

We consider a time-dependent linear convection-diffusion equation. This equation is approximated by a combined finite element-finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements, and the convection term by upwind barycentric finite volumes on a triangular grid. An implicit Euler approach is used for time discretization. It is shown that the error associated with this scheme, measured by a discrete L^~-L^2- and L^2-H^1-norm, respectively, decays linearly with the mesh size and the time step. This result holds without any link between mesh size and time step. The dependence of the corresponding error bound on the diffusion coefficient is completely explicit.