Ivan Hlavacek, Michal Krizek, Mathematical Institute, Academy of Sciences, Zitna 25, CZ-115 67 Praha 1, Czech Republic, e-mail: krizek@earn.cvut.cz, Vladislav Pistora, Institute of Nuclear Research, CZ-250 68 Rez, Czech Republic
Abstract: 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 $\Cal O(h^2)$ 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.
Keywords: weighted averaged gradient, linear elements, nonuniform triangulations, superapproximation, superconvergence
Classification (MSC 1991): 65N30
