How to recover the gradient of linear elements on nonuniform triangulations
Ivan Hlaváček, Michal Křı́žek, Vladislav Pištora · Applications of Mathematics · 1996
We propose and examine a simple averaging formula for the gradient of linear finite elements in $R^d$ whose interpolation order in the $L^q$-norm is $\mathcal O(h^2)$ for $d<2q$ and nonuniform triangulations. For elliptic problems in $R^2$ we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.