Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition

A. Muntean, O. Lakkis

Research output: Book/ReportReportAcademic

149 Downloads (Pure)

Abstract

We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry’s law) posed at air-liquid interfaces. We prove the rate of convergence of the two-scale Galerkin method proposed in [7] for approximating this system in the case when both the microstructure and macroscropic domain are two-dimensional. The main difficulty is created by the presence of a boundary nonlinear term entering the transmission condition. Besides using the particular two-scale structure of the system, the ingredients of the proof include two-scale interpolation-error estimates, an interpolation-trace inequality, and improved regularity estimates.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages14
Publication statusPublished - 2010

Publication series

NameCASA-report
Volume1008
ISSN (Print)0926-4507

Fingerprint

Dive into the research topics of 'Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition'. Together they form a unique fingerprint.

Cite this