Numerical Comparison of Two Stabilized Mixed Finite Element Methods for Convection-Diffusion-Equations on Surfaces

In this paper, the finite element approximation of the convection-diffusion-reaction equation on surfaces is studied. By introducing middle variables of different forms, the original equation is transformed into the equivalent, first-order mixed form. Using the idea of mixed finite element, this paper directly uses the mixed stabilization method of low order finite element pair(P₁-P₁) approximation. The method not only satisfies the well-posed condition, but also can effectively capture the non-physical oscillation caused by convective dominance. Finally, the numerical results show that the convergence results are consistent with the known theory.