A NONCONFORMING WEAK RESIDUAL ERROR ESTIMATOR FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Abstract

A nonconforming weak residual error estimator is presented and analyzed for nite element solutions of linear elliptic partial dierential equations. The treatment of the ux jumps across element edges is of special interest. The estimator is obtained by solving local residual problems which do not explicitly involve the jumps and do not require boundary conditions. The estimator handles both interior and edge residuals on each element by a suitable construction of the basis functions for the local problems. Together with the previous conforming estimator, the weak residual error estimation, without the ux jumps, can thus be applied to both odd- and even-order nite element approximations.