Nonconforming vector finite elements for H(curl;Ω)∩H(div;Ω)H(curl;Ω)∩H(div;Ω)

We present a family of nonconforming vector finite elements of arbitrary order for problems posed on the space H(curl;Ω)∩H(div;Ω), where Ω⊂R2Ω⊂R2. This result was first stated as a conjecture by Brenner and Sung (2009) [1]. In contrast an extension of the same conjecture to domains of R3R3 is disproved.