A stabilized three-field formulation for advection-diffusion equations

In this paper, we propose a new stabilized three-field formulation applied to the advection-diffusion equation. Using finite elements with SUPG stabilization in the interior of the subdomains our approach enables LIS to use almost arbitrary discrete function spaces. They need not to satisfy the inf-sup conditions of the standard three-field formulation. We can prove the stability of the scheme and an I priori estimate which is of the same convergence order as the standard SUPG method. Furthermore, the scheme can be solved efficiently by an adapted Schur complement equation. Finally some numerical experiments confirm our theoretical results.