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 and -norm for various problems with discontinuous coefficient case.
"A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in ." J. Appl. Math. 2020 1 - 8, 2020. https://doi.org/10.1155/2020/2684630