Multilevel Boundary Functionals for Least-squares Mixed Finite Element Methods

For least-squares mixed nite element methods for the rst-order system formulation of second-order elliptic problems, a technique for the weak enforcement of boundary conditions is presented. This approach is based on least-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 ux and standard continuous piecewise linear elements for the pressure, respectively. Continuity and coercivity of the resulting bilinear form is proved implying optimal order convergence of the resulting Galerkin approximation. The boundary least-squares functional is implemented using multilevel principles and the technique is tested numerically for a model problem.