Simple Curl-Curl-Conforming Finite Elements in Two Dimensions

Abstract

We construct smooth finite element de Rham complexes in two space dimensions. This leads to three families of curl-curl-conforming finite elements, two of which contain two existing families. The simplest triangular and rectangular finite elements have only six and eight degrees of freedom, respectively. Numerical experiments for each family demonstrate the convergence and efficiency of the elements for solving the quad-curl problem.