Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes

Abstract

Abstract We construct three H-curl-curl finite elements. The P 2 P_{2} and P 3 P_{3} vector finite element spaces are both enriched by one common P 4 P_{4} bubble and their local degrees of freedom are 13 and 21, respectively. As there does not exist any P 1 P_{1} H-curl-curl conforming finite element, the P 1 P_{1} H-curl-curl nonconforming finite element is constructed with three additional P 4 P_{4} bubbles. Numerical tests are presented, confirming the conformity and the optimal order of convergence.