Abstract
In this paper a Nitsche-type discretization based on discontinuous Galerkin (DG) method for an elliptic three-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polyhedral region Ω which is a union of N disjoint polyhedral subdomains Ω i of diameter O(H i ) and we assume that this partition is geometrically conforming. Inside each subdomain, a conforming finite element space on a quasiuniform triangulation with mesh size O(h i ) is introduced. Large discontinuities on the coefficients and nonmatching meshes are allowed to occur only across ∂ Ω i . In order to deal with the nonconformity of the FE spaces across subdomain interfaces, a discrete problem is formulated using the symmetric interior penalty DG method only on the subdomain interfaces. For solving the resulting discrete system, FETI-DP type of methods are designed and fully analyzed. This paper extends the 2-D results in Dryja et al. (SIAM J. Numer. Anal. 51:400–422, 2013) to 3-D problems.
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References
Dryja, M.: On discontinuous Galerkin methods for elliptic problems with discontinuous coefficients. Comput. Methods Appl. Math. 3(1), 76–85 (2003). Dedicated to Raytcho Lazarov
Dryja, M., Galvis, J., Sarkis, M.: A FETI-DP preconditioner for a composite finite element and discontinuous Galerkin method. SIAM J. Numer. Anal. 51(1), 400–422 (2013). doi:10.1137/100796571. http://dx.doi.org/10.1137/100796571
Toselli, A., Widlund, O.: Domain Decomposition Methods—Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34. Springer, Berlin (2005)
Acknowledgements
The first author has been partially supported by the Polish NSC grant 2011/01/B/ST1/01179.
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Dryja, M., Sarkis, M. (2014). 3-D FETI-DP Preconditioners for Composite Finite Element-Discontinuous Galerkin Methods. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_10
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DOI: https://doi.org/10.1007/978-3-319-05789-7_10
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