On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Ivan Hlaváček, Michal Křı́žek · Applications of Mathematics · 1987
Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate $O(h^{3/2})$ is proved in the $L^2$-norm. For a class of polygonal domains the global estimate $O(h^2)$ can be proven.