A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in ℝ 3

Abstract

In this paper, we suggest a new patch condition for nonconforming mixed finite elements (MFEs) on parallelepiped and provide a framework for the convergence. Also, we introduce a new family of nonconforming MFE space satisfying the new patch condition. The numerical experiments show that the new MFE shows optimal order convergence in $H\left(\text{div}\right)$ and $L^2$-norm for various problems with discontinuous coefficient case.