Geodesic
Two-level additive Schwarz preconditioners for fourth-order mixed methods
Electronic transactions on numerical analysis, Tome 22 (2006), pp. 1-16.

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Summary: A two-level additive Schwarz preconditioning scheme for solving Ciarlet-Raviart, Hermann-Miyoshi, and Hellan-Hermann-Johnson mixed method equations for the biharmonic Dirichlet problem is presented. Using suitably defined mesh-dependent forms, a unified approach, with ties to the work of Brenner for nonconforming methods, is provided. In particular, optimal preconditioning of a Schur complement formulation for these equations is proved on polygonal domains without slits, provided the overlap between subdomains is sufficiently large.
Classification : 65F10, 65N30, 65N55
Keywords: additive Schwarz preconditioner, mixed finite elements, biharmonic equation, domain decomposition, mesh dependent norms 
@article{ETNA_2006__22__a8,
     author = {Hanisch, M.R.},
     title = {Two-level additive {Schwarz} preconditioners for fourth-order mixed methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--16},
     publisher = {mathdoc},
     volume = {22},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__22__a8/}
}
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Hanisch, M.R. Two-level additive Schwarz preconditioners for fourth-order mixed methods. Electronic transactions on numerical analysis, Tome 22 (2006), pp. 1-16. http://geodesic.mathdoc.fr/item/ETNA_2006__22__a8/