A residual based error estimator for mortar finite element discretizations

A residual based error estimator for the approximation of linear elliptic b oundary value problems by nonconforming finite element methods is introduce d and analyzed. In particular, we consider mortar finite element techniques restricting ourselves to geometrically conforming domain decomposition met hods using P1 approximations in each subdomain. Additionally, a residual ba sed error estimator for Crouzeix-Raviart elements of lowest order is presen ted and compared with the error estimator obtained in the more general mort ar situation. It is shown that the computational effort of the error estima tor can be considerably reduced if the special structure of the Lagrange mu ltiplier is taken into account. Mathematics Subject Classification (1991): 65N15, 65N30, 65N50, 65N55.