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arXiv · 1802.04963

Superconvergent recovery of Raviart--Thomas mixed finite elements on triangular grids

Randolph E. Bank·Yuwen Li
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Abstract

For the second lowest-order Raviart--Thomas mixed method, we prove that the canonical interpolant and finite element solution for the vector variable in elliptic problems are superclose in the $H(\text{div})$-norm on mildly structured meshes, where most pairs of adjacent triangles form approximate parallelograms. We then develop a family of postprocessing operators for Raviart--Thomas mixed elements on triangular grids by using the idea of local least squares fittings. Super-approximation property of the postprocessing operators for the lowest and second lowest order Raviart--Thomas elements is proved under mild conditions. Combining the supercloseness and super-approximation results, we prove that the postprocessed solution superconverges to the exact solution in the $L^2$-norm on mildly structured meshes.

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Randolph E. Bank, Yuwen Li. 2019-10-07. Superconvergent recovery of Raviart--Thomas mixed finite elements on triangular grids. https://doi.org/10.1007/s10915-019-01068-0

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