Superconvergent recovery of Raviart--Thomas mixed finite elements on triangular grids
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 -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 -norm on mildly structured meshes.
Keywords
Cite
@article{arxiv.1802.04963,
title = {Superconvergent recovery of Raviart--Thomas mixed finite elements on triangular grids},
author = {Randolph E. Bank and Yuwen Li},
journal= {arXiv preprint arXiv:1802.04963},
year = {2019}
}