# Simplex-averaged Finite Element Methods for H(grad), H(curl) and H(div) Convection-diffusion Problems

## Meeting Details

Abstract: This talk is devoted to the construction and analysis of a finite element approximation for the H(D) convection-diffusion problem, where D can be chosen as $grad$, $curl$ or $div$ in 3D case. An essential feature of this construction is to properly average the PDE coefficients on the sub-simplexes. The scheme is of the class of exponentially fitted method that results in a special upwinding scheme when the diffusion coefficient approaches to zero. The well-posedness is established for sufficiently small mesh size assuming that the convection-diffusion problem is uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate its robustness and effectiveness for general convection-diffusion problems.