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

Abstract

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

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