Abstract
In this article we solve the diffusion-advection-reaction model problem with Robin boundary conditions in an open bounded domain Ω∈Rn, with n=1,2,3. For the discretization, we use the mixed-hybrid finite element method of lowest order on a simplicial partition of Ω¯. To prevent the occurrence of spurious unphysical oscillations we numerically evaluate the local bilinear form with a quadrature that is equivalent to introducing an optimal amount of artificial diffusion on each edge of the simplex. The resulting scheme is monotone and flux-conservative and is able to compute accurate solutions even with a corse mesh. The robustness and accuracy of the method is demonstrated on examples in Rn, n=1,2,3, characterized by the presence of steep boundary and internal layers.