Superconvergence results on mildly structured triangulations (Q1581960)

The paper is concerned with improvements of the classical \(O(h)\)-convergence of the gradients (e.g. linear) finite element approximations to the gradient of the exact solution of a second-order elliptic problem. For this purpose, recovered gradients are investigated which have this superconvergence property, and are obtained e.g. by appropriate averaging processes across element edges. Recovered gradients were known to provide \(O(h^2)\)-convergence for fully structured and strongly structured meshes; in this paper, generalizations to ``mildly'' structured meshes are presented. In particular, superconvergence is shown to be preserved, for certain meshes, after local refinement.