Superconvergent flux recovery of the Rannacher-Turek nonconforming element

Abstract

This work presents superconvergence estimates of the nonconforming Rannacher--Turek element for second order elliptic equations on any cubical meshes in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. In particular, a corrected numerical flux is shown to be superclose to the Raviart--Thomas interpolant of the exact flux. We then design a superconvergent recovery operator based on local weighted averaging. Combining the supercloseness and the recovery operator, we prove that the recovered flux superconverges to the exact flux. As a by-product, we obtain a superconvergent recovery estimate of the Crouzeix--Raviart element method for general elliptic equations.

21 pages

References in corpus (2)

• Global superconvergence of the lowest order mixed finite element on mildly structured meshes
• Superconvergent recovery of Raviart--Thomas mixed finite elements on triangular grids

Cited by in corpus (1)

• Recovery-based a posteriori error analysis for plate bending problems