Overlapping Schwarz preconditioners for Fekete spectral elements

We construct and study overlapping Schwarz preconditioners for the iterative solution of elliptic problems discretized with spectral elements based on Fekete nodes (TSEM). These are a generalization to non-tensorial elements of the classical Gauss-Lobatto-Legendre hexahedral spectral elements (QSEM). Even if the resulting discrete problem is more ill-conditioned than in the classical QSEM case, the resulting preconditioned algorithm using generous overlap is optimal and scalable, since its convergence rate is bounded by a constant independent of the number of elements, subdomains and polynomial degree employed.