Two New Enriched Multiscale Coarse Spaces for the Additive Average Schwarz Method

In this paper we introduce an Average Additive Schwarz method with spectrally enriched coarse grids for a standard Finite Element discretization of a second order elliptic problem with discontinuous coefficients, where the discontinuities are inside subdomains and across subdomain boundaries. The proposed methods depend linearly on the mesh parameters H∕h, i.e., depending on the distribution of the coefficient in the model problem, the parameters describing the convergence of the PCG method used to solve the preconditioned system depends linearly or on the mesh parameters. In case when the coarse space is large enough the convergence of the PCG method is independent of jumps in the coefficient.