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A mixed adaptive variational multiscale method with applications in oil reservoir simulation
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2009 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 19, no 7, 1017-1042 p.Article in journal (Refereed) PublishedText
Abstract [en]

We present a mixed adaptive variational multiscale method for solving elliptic second-order problems. This work is an extension of the adaptive variational multiscale method (AVMS), introduced by Larson and Malqvist,(15-17) to a mixed formulation. The method is based on a particular splitting into coarse and fine scales together with a systematic technique for approximation of the fine scale part based on solution of decoupled localized subgrid problems. We present the mixed AVMS method and derive a posteriori error estimates both for linear functionals and the energy norm. Based on the estimates we propose adaptive algorithms for automatic tuning of critical discretization parameters. Finally, we present numerical examples on a two-dimensional slice of an oil reservoir.

Place, publisher, year, edition, pages
World Scientific, 2009. Vol. 19, no 7, 1017-1042 p.
Keyword [en]
Variational multiscale method, mixed formulation, a posteriori error estimate, adaptive methods
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-115990DOI: 10.1142/S021820250900370XISI: 000269124700001OAI: oai:DiVA.org:umu-115990DiVA: diva2:907068
Available from: 2016-02-26 Created: 2016-02-08 Last updated: 2016-02-26Bibliographically approved

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Larson, Mats G
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Department of Mathematics and Mathematical Statistics
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