Low Order Crouzeix-Raviart Type Nonconforming Finite Element Methods for Approximating Maxwell's Equations

Abstract

The aim of this paper is to study the convergence analysis of three low order Crouzeix-Raviart type nonconforming rectangular finite elements to Maxwell's equations, on a mixed finite element scheme and a finite element scheme, respectively. The error estimates are obtained for one of above elements with regular meshes and the other two under anisotropic meshes, which are as same as those in the previous literature for conforming elements under regular meshes.