A stabilized finite element method for advection-diffusion equations on surfaces

A recently developed Eulerian finite element method (FEM) is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, FEMs tend to be unstable unless the mesh is sufficiently fine. The paper introduces a stabilized FE formulation based on the streamline upwind Petrov-Galerkin (SUPG) technique. An error analysis of the method is given. Results of numerical experiments are presented, which illustrate the performance of the stabilized method.