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...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on numerical analysis 2014-01, Vol.52 (4), p.1497-1524
Main Authors: Japhet, Caroline, Maday, Yvon, Nataf, Frédéric
Format: Article
Language:English
Subjects:
Convergence
Error analysis
Finite element method
Mathematical analysis
Mathematical models
Mortars
Numerical analysis
Polynomials
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0036-1429
1095-7170
DOI:10.1137/130912621