Superconvergence of the gradient of Galerkin approximations for elliptic problems (Q5903603)

A finite element method for the Dirichlet problem on a square for the equation \(-\Delta u+bu=f\) (b\(\geq 0)\) is considered. It is based on using tensor products of continuous piecewise polynomial spaces. The author shows that a superconvergence phenomenon for the averaged gradient occurs only in case of odd degree polynomials. Numerical examples are given as well.