A Finite Element-Finite Volume Discretization of Convection-Diffusion-Reaction Equations with Nonhomogeneous Mixed Boundary Conditions: Error Estimates

摘要

We consider a time-dependent and a steady linear convection-diffusion-reaction equation whose coefficients are nonconstant. Boundary conditions are mixed (Dirichlet and Robin-Neumann) and nonhomogeneous. Both the unsteady and the steady problem 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. The L-2(H-1) - and the L-infinity(L-2) - error in the unsteady case and the H-1-error in the steady one are estimated against the data, in such a way that no parameter enters exponentially into the constants involved. (C) 2016 Wiley Periodicals, Inc.