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Keywords:
weighted averaged gradient; linear elements; nonuniform triangulations; superapproximation; superconvergence
Summary:
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.
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