On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
Ivan Hlaváček, Michal Křı́žek · Applications of Mathematics · 1987
Second order elliptic systems with boundary conditions of Dirichlet, Neumann's or Newton's type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order $O(h^2)$ are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.