Overlapping Schwarz methods in H(curl) on polyhedral domains

We consider domain decomposition preconditioners for the linear algebraic equations which result from finite element discretization of problems involving the bilinear form α (·, ·) + ( curl ·, curl ·) defined on a polyhedral domain Ω. Here (·, ·) denotes the inner product in ( L 2 (Ω)) 3 and is α positive number. We use Nedelec's curl-conforming finite elements to discretize the problem. Both additive and multiplicative overlapping Schwarz preconditioners are studied. Our results are uniform with respect to the mesh size and α under standard assumptions concerning the overlapping subdomains.