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Journal of Scientific Computing

, Volume 81, Issue 3, pp 1882–1905 | Cite as

Superconvergent Recovery of Raviart–Thomas Mixed Finite Elements on Triangular Grids

  • Randolph E. Bank
  • Yuwen LiEmail author
Article
  • 156 Downloads

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 \(H({{\,\mathrm{div}\,}})\)-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.

Keywords

Superconvergence Mildly structured grids Mixed methods Raviart–Thomas elements Second order elliptic equations 

Mathematics Subject Classification

65N30 65N50 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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