Accelerating the method of finite element patches using approximately harmonic functions

This is the authors' abstract. We don't add key points for this paper.

We present a new variant of a domain decomposition method with complete overlap and not necessarily nested grids to solve numerically elliptic problems with multi-scale data. The novelty of the method consists in restricting finite element functions on the coarse grid to be approximately harmonic inside the subdomain where a finer triangulation is applied. Numerical experiments confirm an increase in the convergence rate over a previously proposed method.