Geodesic
An iterative substructuring algorithm for a \(C^{0}\) interior penalty method
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 313-332
We study an iterative substructuring algorithm for a $C^0$ interior penalty method for the biharmonic problem. This algorithm is based on a Bramble-Pasciak-Schatz preconditioner. The condition number of the preconditioned Schur complement operator is shown to be bounded by $C \left(1+\ln(\tfrac{H}{h})\right)^2$, where $h$ is the mesh size of the triangulation, $H$ represents the typical diameter of the nonoverlapping subdomains, and the positive constant $C$ is independent of $h, H,$ and the number of subdomains. Corroborating numerical results are also presented.
Classification : 65N55, 65N30
Keywords: biharmonic problem, iterative substructuring, domain decomposition, $C^0$ interior penalty methods, discontinuous Galerkin methods 
@article{ETNA_2012__39__a8,
     author = {Brenner,  Susanne C. and Wang,  Kening},
     title = {An iterative substructuring algorithm for a {\(C^{0}\)} interior penalty method},
     journal = {Electronic transactions on numerical analysis},
     pages = {313--332},
     year = {2012},
     volume = {39},
     zbl = {1321.65181},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a8/}
}
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AU  - Wang,  Kening
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SP  - 313
EP  - 332
VL  - 39
UR  - http://geodesic.mathdoc.fr/item/ETNA_2012__39__a8/
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%A Brenner,  Susanne C.
%A Wang,  Kening
%T An iterative substructuring algorithm for a \(C^{0}\) interior penalty method
%J Electronic transactions on numerical analysis
%D 2012
%P 313-332
%V 39
%U http://geodesic.mathdoc.fr/item/ETNA_2012__39__a8/
%G en
%F ETNA_2012__39__a8
Brenner,  Susanne C.; Wang,  Kening. An iterative substructuring algorithm for a \(C^{0}\) interior penalty method. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 313-332. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a8/