Lower Bounds for Eigenvalues of Elliptic Operators by Overlapping Domain Decomposition

In this paper, we consider a new approach to estimation from below of the lowest eigenvalues of symmetric positive definite elliptic operators. The approach is based on the overlapping domain decomposition procedure and on the replacement of subdomain operators by special low rank perturbed scalar operators. The algorithm is illustrated by applications to model problems with mixed boundary conditions and strongly discontinuous coefficients.