A family of even-order edge-oriented nonconforming finite elements in 2D with efficient locally conservative flux reconstruction

Abstract

In this paper, we propose a new family of edge-oriented even-order nonconforming finite elements in 2D. The proposed element has fewer degrees of freedom compared to the existing edge-oriented nonconforming elements, and preserves some attractive properties of the Crouzeix-Raviart element, such as the optimal approximation capability and the inf-sup stability. We also present an efficient $H\left(\mathrm{div}\right)$-conforming flux reconstruction for the finite element discretization by the proposed element, which is possible due to its edge-oriented degrees of freedom.