New curl conforming finite elements on parallelepiped

Abstract

In this paper, we introduce new curl conforming elements of higher order on parallelepiped. This element has smaller number of degrees of freedom than the well known Nedelec spaces do, however, one can still obtain the same convergence order. To prove error estimate for curl conforming finite element methods, we also define the corresponding divergence conforming elements. Some efficient way of implementing our element is discussed in Remarks 2 and 3.