A gradient recovery approach for nonconforming finite element methods with boundary modification

Gradient Recovery Approach for Non-Conforming Finite Element

Abstract

We use orthogonal and biorthogonal projections to post-process the gradient of the finite element solution produced by a non-conforming finite element approach. This leads to a better approximation property of the recovered gradient. We use an L2-projection, where the trial and test spaces are different but form a biorthogonal system. This leads to an efficient numerical approach. We also modify our projection by applying the boundary modification method to obtain a higher order approximation on the boundary patch. Numerical examples are presented to demonstrate the efficiency and optimality of the approach.

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