Primal and mixed upwind finite element approximations of control advection-diffusion problems

Abstract

Control advection-diffusion problems are formulated via variational inequalities and effective upwind finite element approximations are studied. The method of local subdifferentials is applied to model and dualize control constraints, as well as to produce global primal and mixed variational formulations. Upwind finite element schemes are derived, satisfying the discrete maximum principle and the conservation of mass law. The numerical resolution methods used are iterative algorithms of the Uzawa type, which are formulated and analyzed. Some numerical experiments are presented for a model discrete problem.