An exponential-fitting finite element method for convection-diffusion problems

In this paper we consider an exponential fitting finite element method (EFFEM) for the discretization of convection dominated convection-diffusion equation. Hemker's basis functions [5] are very robust for solving the one-dimensional problem. However, they cannot resolve the two dimensional problem well. The EFFEM provides an exponential fitting for the solution on each grid to stabilize the solution. The error bound for the EFFEM in the energy norm is in the order of Oh/εe-ch/ε for uniform mesh size h on the bilinear elements. We compare the performance of the EFFEM with various streamline upwind schemes, and it shows that the exponential terms of the basis functions are tailored the solution accurately in the flow direction. Our numerical results demonstrate the efficiency and accuracy of the proposed method.