Geodesic
Cross-points in domain decomposition methods with a finite element discretization
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 219-240
Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to allow for convergence to the underlying mono-domain solution. Well-known such non-overlapping methods are the Dirichlet-Neumann method, the FETI and Neumann-Neumann methods, and optimized Schwarz methods. For all these methods, cross-points in the domain decomposition configuration where more than two subdomains meet do not pose any problem at the continuous level, but care must be taken when the methods are discretized. We show in this paper two possible approaches for the consistent discretization of Neumann conditions at cross-points in a finite element setting: the auxiliary variable method and complete communication.
Classification : 65N55, 65N30, 65F10
Keywords: domain decomposition, cross-points, finite element discretization, auxiliary variables, complete communication 
@article{ETNA_2016__45__a14,
     author = {Gander,  Martin J. and Santugini,  K\'evin},
     title = {Cross-points in domain decomposition methods with a finite element discretization},
     journal = {Electronic transactions on numerical analysis},
     pages = {219--240},
     year = {2016},
     volume = {45},
     zbl = {1347.65187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a14/}
}
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AU  - Santugini,  Kévin
TI  - Cross-points in domain decomposition methods with a finite element discretization
JO  - Electronic transactions on numerical analysis
PY  - 2016
SP  - 219
EP  - 240
VL  - 45
UR  - http://geodesic.mathdoc.fr/item/ETNA_2016__45__a14/
LA  - en
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%0 Journal Article
%A Gander,  Martin J.
%A Santugini,  Kévin
%T Cross-points in domain decomposition methods with a finite element discretization
%J Electronic transactions on numerical analysis
%D 2016
%P 219-240
%V 45
%U http://geodesic.mathdoc.fr/item/ETNA_2016__45__a14/
%G en
%F ETNA_2016__45__a14
Gander,  Martin J.; Santugini,  Kévin. Cross-points in domain decomposition methods with a finite element discretization. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 219-240. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a14/