Volume 41, pp. 109-132, 2014.

Error estimates for a two-dimensional special finite element method based on component mode synthesis

Ulrich Hetmaniuk and Axel Klawonn


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.

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Key words

domain decomposition, finite elements, eigendecomposition, a posteriori error estimation

AMS subject classifications

35J20, 65F15, 65N25, 65N30, 65N55

ETNA articles which cite this article

Vol. 48 (2018), pp. 156-182 Alexander Heinlein, Axel Klawonn, Jascha Knepper, and Oliver Rheinbach: Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D
Vol. 54 (2021), pp. 234-255 Susanne C. Brenner, José C. Garay, and Li-yeng Sung: Additive Schwarz preconditioners for a localized orthogonal decomposition method

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