A stabilized scheme for the lagrange multiplier method for advection-diffusion equations

Abstract

We consider a new stabilized finite element method for advection-diffusion equations, where the Dirichlet boundary condition is imposed in a weak sense by Lagrange multipliers. The inf-sup condition of the corresponding mixed problem is circumvented by adding some further terms. Using the SUPG-stabilization, an optimal a priori estimate is shown for the singularly perturbed case. Then we present an a posteriori error estimator for our stabilized scheme. Some numerical experiments support the theoretical results. The present results are basic for a nonconforming three-field formulation of the problem.