Geodesic
Error estimates for a two-dimensional special finite element method based on component mode synthesis
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 109-132
This paper presents a priori error estimates for a special finite element discretization based on component mode synthesis. The basis functions exploit an orthogonal decomposition of the trial subspace to minimize the energy and are expressed in terms of local eigenproblems. The a priori error bounds state the explicit dependency of constants with respect to the mesh size and the first neglected eigenvalues. A residual-based a posteriori error indicator is derived. Numerical experiments on academic problems illustrate the sharpness of these bounds.
Classification : 35J20, 65F15, 65N25, 65N30, 65N55
Keywords: domain decomposition, finite elements, eigendecomposition, a posteriori error estimation 
@article{ETNA_2014__41__a18,
     author = {Hetmaniuk,  Ulrich and Klawonn,  Axel},
     title = {Error estimates for a two-dimensional special finite element method based on component mode synthesis},
     journal = {Electronic transactions on numerical analysis},
     pages = {109--132},
     year = {2014},
     volume = {41},
     zbl = {1296.65147},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a18/}
}
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AU  - Klawonn,  Axel
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EP  - 132
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UR  - http://geodesic.mathdoc.fr/item/ETNA_2014__41__a18/
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%0 Journal Article
%A Hetmaniuk,  Ulrich
%A Klawonn,  Axel
%T Error estimates for a two-dimensional special finite element method based on component mode synthesis
%J Electronic transactions on numerical analysis
%D 2014
%P 109-132
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%U http://geodesic.mathdoc.fr/item/ETNA_2014__41__a18/
%G en
%F ETNA_2014__41__a18
Hetmaniuk,  Ulrich; Klawonn,  Axel. Error estimates for a two-dimensional special finite element method based on component mode synthesis. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 109-132. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a18/