Multiscale analysis and simulation of a reaction-diffusion problem with transmission conditions
type: Item
instance of: scholarly article
title: Multiscale analysis and simulation of a reaction-diffusion problem with transmission conditions
zbMATH Open document ID: 1228.35030
author: Maria Neuss-Radu
author: Stephan Ludwig
author: Willi Jäger
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-11-05T00:00:00Z
review text: The multiscale method as a form of homogenization technique is used by the authors for finding solutions to reaction-diffusion problems with some transmission conditions. The paper is well organized and the appropriate references acknowledged. The variational formulation of the problem is stated nicely and is is shown that the sequence \((u^+_{0N}, u^-_{0N}, u_N^M)\) is bounded in the appropriate spaces, enabling them to extract subsequences which converge weakly in the chosen spaces. This enables the authors to obtain the unique weak solution and hence the convergence of the whole sequence of Galerkin approximates. They finally illustrate their results by means of numerical simulations.
reviewed by: Emmanuel K. Essel
Mathematics Subject Classification ID: 35B27
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 5810876
zbMATH Keywords: numerical multiscale analysis
zbMATH Keywords: unique weak solution
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.11.024
OpenAlex ID: W2147811950
cites work: Effective Transmission Conditions for Reaction-Diffusion Processes in Domains Separated by an Interface
cites work: High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales
cites work: Q5890172
DOI: 10.1016/J.NONRWA.2008.11.024
description: scientific article; zbMATH DE number 5810876