A MULTILEVEL DECOMPOSITION RESULT IN H(curl)

Abstract. Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. The arising linear equation systems are usually huge and thus require iterative solvers with good pre-conditioners. In [10] and [1] multigrid preconditioners for Maxwell equations have been developed and analyzed. In the current pa-per, we improve the results available so far. The key is to utilize recently proposed Clément type interpolation operators in H(curl) which allow an analysis very similar to the scalar case. The present improvement involves commuting operators which are projections. 1