# Nonoverlapping Three Grid Additive Schwarz for hp-DGFEM with Discontinuous Coefficients

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## Abstract

We discuss a nonoverlapping additive Schwarz method for an *h*-*p* DGFEM discretization of an elliptic PDE with discontinuous coefficients, where the fine grid is decomposed into subdomains of size *H* and the coarse grid consists of cells size \(\mathcal {H}\) such that \(h\leq H \leq \mathcal {H}\). We prove the condition number is \(O(p^2/q)\cdot O(\mathcal {H}^2/Hh)\) and is independent from the jumps of the coefficient if the discontinuities are aligned with the coarse grid.

## Notes

### Acknowledgements

The author wishes to thank two anonymous referees whose comments and remarks helped to improve the paper substantially. This research has been partially supported by the Polish National Science Centre grant 2016/21/B/ST1/00350.

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