Hierarchical a posteriori error estimators for mortar finite element methods with Lagrange multipliers

Hierarchical a posteriori error estimators are introduced and analyzed for mor' tar finite element methods. A weak continuity condition at the interfaces is enforced by means of Lagrange multipliers. The two proposed error estimators are based on a defect correction in higher-order finite element spaces and an adequate hierarchical two-level splitting. The first provides upper and lower bounds for the discrete energy norm of the mortar finite element solution whereas the second also estimates the error for the Lagrange multiplier. It is shown that an appropriate measure for the nonconformity of the mortar finite element solution is the weighted L²-norm of the jumps across the interfaces.