T.V. Kolev, J.E. Pasciak, and P.S. Vassilevski
This paper analyzes a two--level preconditioning scheme for $\Hcurl$ forms. The scheme utilizes an auxiliary problem on a related mesh that is more amenable for constructing optimal order multigrid methods. More specifically, we analyze the case when the auxiliary mesh can only approximately cover the original domain. The latter assumption is important since it allows for easy construction of nested multilevel spaces on the auxiliary mesh. Numerical experiments in both 2 and 3 space dimensions illustrate the optimal performance of the method.