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Error control based model reduction for multiscale problems. (English) Zbl 1278.15008

Handlovičová, Angela (ed.) et al., Algoritmy 2012. 19th conference on scientific computing, Vysoké Tatry, Podbanské, Slovakia, September 9–14, 2012. Proceedings of contributed papers and posters. Bratislava: Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry (ISBN 978-80-227-3742-5/pbk). 1-10 (2012).
Summary: In this contribution we review a posteriori based discretization methods for variational multiscale problems and suggest a suitable conceptual approach for an efficient numerical treatment of parametrized variational multiscale problems where the parameters are either chosen from a low dimensional parameter space or consists of parameter functions from some compact low dimensional manifold that is embedded in some high dimensional or even infinite dimensional function space. The approach is based on combinations of ideas from established numerical multiscale methods and efficient model reduction approaches such as the reduced basis method.
For the entire collection see [Zbl 1260.00028].

MSC:

15A15 Determinants, permanents, traces, other special matrix functions
15A09 Theory of matrix inversion and generalized inverses
15A23 Factorization of matrices

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