Abstract
In this paper, a superconvergence result of the Crouzeix-Raviart element method is derived for the second-order elliptic equation on the uniform triangular meshes, in which any two adjacent triangles form a parallelogram. A local weighted averaging post-processing algorithm for the numerical stress is presented. Based on the equivalence between the Crouzeix-Raviart element method and the lowest order Raviart-Thomas element method, we prove that the error between the exact stress and the postprocessed numerical stress is of order h3/2. Two numerical examples are presented to confirm the theoretical result.
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