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A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1752-1211
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).ORCID iD: 0000-0002-1160-0007
2018 (English)In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 39, no 4, p. 413-437Article in journal (Refereed) Published
Abstract [en]

We study the approximation of a multiscale reaction–diusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro– macro ux conditions. Our target system has a typical structure for reaction–diusion ow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semidiscrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally ecient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a ne bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions. A

Place, publisher, year, edition, pages
Taylor & Francis, 2018. Vol. 39, no 4, p. 413-437
Keywords [en]
Feedback nite element method, Galerkin approximation, micro–macro coupling, multiscale reaction–diusion systems
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-62808DOI: 10.1080/01630563.2017.1369996OAI: oai:DiVA.org:kau-62808DiVA, id: diva2:1136115
Available from: 2017-08-25 Created: 2017-08-25 Last updated: 2018-05-22Bibliographically approved

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Lind, MartinMuntean, Adrian

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