A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems

Lind, Martin,1985-Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013) (author)

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

Muntean, Adrian,1974-Karlstads universitet,Institutionen för matematik och datavetenskap (from 2013)(Swepub:kau)adrimunt (author)
Karlstads universitetInstitutionen för matematik och datavetenskap (from 2013) (creator_code:org_t)

In:Numerical Functional Analysis and Optimization: Taylor & Francis39:4, s. 413-4370163-05631532-2467

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