Multilevel boundary functionals for least-squares mixed finite element methods

For least-squares mixed finite element methods for the first-order system f ormulation of second-order elliptic problems, a technique for the weak enfo rcement of boundary conditions is presented. This approach is based on leas t-squares boundary functionals, which are equivalent to the H-1/2 and H-1/2 norms on the trace spaces of lowest-order Raviart-Thomas elements for the flux and standard continuous piecewise linear elements for the pressure, re spectively. Continuity and coercivity of the resulting bilinear form is pro ved implying optimal order convergence of the resulting Galerkin approximat ion. The boundary least-squares functional is implemented using multilevel principles and the technique is tested numerically for a model problem.