High-order finite element methods based on spectral elements or hp-version finite elements improve the accuracy of the discrete solution by increasing the polynomial degree p of the basis functions as well as decreasing the element size h. The discrete systems generated by these high-order methods are much more ill-conditioned than the ones generated by standard low-order finite elements. In this paper, we will focus on spectral elements based on Gauss-Lobatto-Legendre (GLL) quadrature and construct nonoverlapping domain decomposition methods belonging to the family of Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) methods; see [4, 9, 7]. We will also consider inexact versions of the FETI-DP methods, i.e., irFETI-DP and iFETI-DP, see [8]. We will show that these methods are scalable and have a condition number depending only weakly on the polynomial degree.
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Klawonn, A., Rheinbach, O., Pavarino, L.F. (2008). Exact and Inexact FETI-DP Methods for Spectral Elements in Two Dimensions. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_32
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