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We construct three H-curl-curl finite elements. TheP2P_{2}andP3P_{3}vector finite element spaces are both enriched by one commonP4P_{4}bubble and their local degrees of freedom are 13 and 21, respectively. As there does not exist anyP1P_{1}H-curl-curl conforming finite element, theP1P_{1}H-curl-curl nonconforming finite element is constructed with three additionalP4P_{4}bubbles. Numerical tests are presented, confirming the conformity and the optimal order of convergence.

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