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An adaptive variational multiscale method for convection-diffusion problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2009 (English)In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 25, no 1, 65-79 p.Article in journal (Refereed) PublishedText
Abstract [en]

The adaptive variational multiscale method is an extension of the variational multiscale method where the line-scale part of the solution is approximated by a sum of numerically computed solutions to localized subgrid problems. Furthermore, the crucial discretization parameters are chosen automatically by an adaptive algorithm based on a posteriori error estimates. This method has been developed for diffusion-dominated problems and applied to multiscale problems that arise in oil reservoir Simulation. In this paper, we extend the method to convection-diffusion problems. We present it duality based a posteriori error representation formula and an adaptive algorithm that tunes the fine-scale mesh size and the patch sizes of the local problems. Numerical results show rapid convergence of the adaptive algorithm. Copyright (c) 2008 John Wiley & Sons, Ltd.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2009. Vol. 25, no 1, 65-79 p.
Keyword [en]
variational multiscale method, adaptivity, error estimation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-116034DOI: 10.1002/cnm.1106ISI: 000262273800005OAI: oai:DiVA.org:umu-116034DiVA: diva2:904154
Available from: 2016-02-18 Created: 2016-02-08 Last updated: 2016-02-18Bibliographically approved

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Larson, Mats G
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Department of Mathematics and Mathematical Statistics
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