On a global superconvergence of the gradient of linear triangular elements (Q1082054)

We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the \(L^ 2\)-norm than the piecewise constant gradient of the Ritz-Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.