Geodesic
Edge-based Schwarz methods for the Crouzeix-Raviart finite volume element discretization of elliptic problems
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 443-461
In this paper, we present two variants of the additive Schwarz method for a Crouzeix-Raviart finite volume element (CRFVE) discretization of second-order elliptic problems with discontinuous coefficients, where the discontinuities may be across subdomain boundaries. The preconditioner in one variant is symmetric, while in the other variant it is nonsymmetric. The proposed methods are quasi optimal, in the sense that the convergence of the preconditioned GMRES iteration in both cases depend only poly-logarithmically on the ratio of the subdomain size to the mesh size.
Classification : 65F10, 65N22, 65N30, 63N55
Keywords: domain decomposition, Crouzeix-Raviart element, additive Schwarz method, finite volume element, GMRES 
@article{ETNA_2015__44__a9,
     author = {Loneland,  Atle and Marcinkowski,  Leszek and Rahman,  Talal},
     title = {Edge-based {Schwarz} methods for the {Crouzeix-Raviart} finite volume element discretization of elliptic problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {443--461},
     year = {2015},
     volume = {44},
     zbl = {1327.65066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a9/}
}
TY  - JOUR
AU  - Loneland,  Atle
AU  - Marcinkowski,  Leszek
AU  - Rahman,  Talal
TI  - Edge-based Schwarz methods for the Crouzeix-Raviart finite volume element discretization of elliptic problems
JO  - Electronic transactions on numerical analysis
PY  - 2015
SP  - 443
EP  - 461
VL  - 44
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__44__a9/
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%0 Journal Article
%A Loneland,  Atle
%A Marcinkowski,  Leszek
%A Rahman,  Talal
%T Edge-based Schwarz methods for the Crouzeix-Raviart finite volume element discretization of elliptic problems
%J Electronic transactions on numerical analysis
%D 2015
%P 443-461
%V 44
%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a9/
%G en
%F ETNA_2015__44__a9
Loneland,  Atle; Marcinkowski,  Leszek; Rahman,  Talal. Edge-based Schwarz methods for the Crouzeix-Raviart finite volume element discretization of elliptic problems. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 443-461. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a9/