Abstract
Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis methods is a suitable means to reduce computational time. In this proceedings, we show the applicability of the reduced basis framework to a finite volume scheme of a parametrized and highly nonlinear convection-diffusion problem with discontinuous solutions. The complexity of the problem setting requires the use of several new techniques like parametrized empirical operator interpolation, efficient a posteriori error estimation and adaptive generation of reduced data. The latter is usually realized by an adaptive search for base functions in the parameter space. Common methods and effects are shortly revised in this presentation and supplemented by the analysis of a new strategy to adaptively search in the time domain for empirical interpolation data.
MSC2010: 65M08, 65J15, 65Y2
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Acknowledgements
This work was supported by the German Science Foundation (DFG) under the contract number OH 98/2-1. The second author was supported by the Baden Württemberg Stiftung gGmbH.
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Drohmann, M., Haasdonk, B., Ohlberger, M. (2011). Adaptive Reduced Basis Methods for Nonlinear Convection–Diffusion Equations. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_39
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DOI: https://doi.org/10.1007/978-3-642-20671-9_39
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