Abstract
A second order elliptic problem with piecewise constant coefficient in 2-D or 3-D is considered. The problem is discretized by a composite \(h\)-\(p\) finite element method, using continuous functions in subregions where the coefficient is constant and applying discontinuous Galerkin interior penalty method to couple them. The resulting discrete problem is solved by a two-level nonoverlapping additive Schwarz method. Condition number estimate of the preconditioned system, depending on the relative sizes of the underlying grids and on the relative degrees of finite elements used on the fine and coarse grids, is provided. In particular, the rate of convergence of the method is independent of the jumps of the coefficient.
This research has been partially supported by the Polish National Science Centre grant 2011/01/B/ST1/01179.
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Acknowledgement
The author would like to thank Max Dryja for comments on an early draft of the paper. This research has been partially supported by the Polish National Science Centre grant 2011/01/B/ST1/01179.
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Krzyżanowski, P. (2016). Additive Nonoverlapping Schwarz for h-p Composite Discontinuous Galerkin. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_38
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DOI: https://doi.org/10.1007/978-3-319-32152-3_38
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