A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems

• 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

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Feedback nite element method

Galerkin approximation

micro–macro coupling

multiscale reaction–diusion systems

Matematik

Mathematics

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