Overlapping Schwarz methods in H(curl) on polyhedral domains

Abstract

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 (L2(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.