Title: Overlapping Schwarz Preconditioners for Spectral Nedelec Elements for a Model Problem in H(curl) (NYU-CS-TR834) Author: Bernhard Hientzsch Abstract: A two-level overlapping domain decomposition method is analyzed for a Nedelec spectral element approximation of a model problem appearing in the solution of Maxwell's equations. The overlap between subdomains can consist of entire spectral elements or rectangular subsets of spectral elements. For fixed relative overlap and overlap made from entire elements, the condition number of the method is bounded, independently of the mesh size, the number of subregions, the coefficients and the degree of the spectral elements. In the case of overlap including just parts of spectral elements, a bound linear in the degree of the elements is proven. It is assumed that the coarse and fine mesh are quasi-uniform and shape-regular and that the domain is convex. Arguments that would not require quasi-uniformity of the coarse mesh and convexity of the domain are mentioned. Our work generalizes results obtained for lower-order Nedelec elements in Toselli [Numerische Mathematik (2000) 86:733-752]. Numerical results for the two-level algorithm in two dimensions are also presented, supporting our analysis.