Robin Schwarz Algorithm for the NICEM Method: The $\mathbf{P}_q$ Finite Element Case

In [M. J. Gander et al., in Domain Decomposition Methods in Science and Engineering, Lect. Notes Comput. Sci. Eng. 40, Springer-Verlag, Berlin, 2005, pp. 259--266; C. Japhet, Y. Maday, and F. Nataf, Math. Models Methods Appl. Sci., 23 (2013), pp. 2253--2292] we proposed a new nonconforming domain decomposition paradigm, the new interface cement equilibrated mortar method, based on Schwarz-type methods, that allows for the use of Robin interface conditions on nonconforming grids. The error analysis was done for $\mathbf{P}_1$ finite elements, in two and three dimensions. In this paper, we provide new numerical analysis results that allow us to extend this error analysis in two dimensions for piecewise polynomials of higher order and also prove the convergence of the iterative algorithm in all these cases.

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