Superconvergence analysis of approximate boundary-flux calculations

Summary Certain projection post-processing techniques have been proposed for computing the boundary flux for two-dimensional problems (e.g., see Carey, et al. 5]). In a series of numerical experiments on elliptic problems they observed that these post-processing formulas for approximate fluxes were almost (O(h ²)-accurate for linear triangular elements. In this paper we prove that the computed boundary flux isO(h ² ln 1/h)-accurate in the maximum norm for the partial method of 5]. If the solutionuH ³() then the boundary flux error isO(h ^3/2) in theL ²-norm.