GOAL-ORIENTED LOCAL A POSTERIORI ERROR ESTIMATORS FOR H(div) LEAST-SQUARES FINITE ELEMENT METHODS

We propose a goal-oriented, local a posteriori error estimator for H(div) least-squares (LS) finite element methods. Our main interest is to develop an a posteriori error estimator for the flux approximation in a preassigned region of interest D subset of Omega. The estimator is obtained from the LS functional by scaling residuals with proper weight coefficients. The weight coefficients are given in terms of local mesh size h(T) and a function omega(D) depending on the distance to D. This new error estimator measures the pollution effect from the outside region of D and provides a basis for local refinement in order to efficiently approximate the solution in D. Numerical experiments show superior performances of our goal-oriented a posteriori estimators over the standard LS functional and global error estimators.