Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure -- efficient solution strategies based on homogenization theory

DOI10.3934/naco.2016008zbMath1354.34058OpenAlexW2492366084MaRDI QIDQ317140

Silja Meyer-Nieberg, Gerhard-Wilhelm Weber, Erik Kropat

Publication date: 30 September 2016

Published in: Numerical Algebra, Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/naco.2016008

zbMATH Keywords

microstructuressingular perturbationsasymptotic analysistwo-scale convergenceboundary value problems on graphs and networksdiffusion-advection-reaction equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multiple scale methods for ordinary differential equations (34E13) Boundary value problems on graphs and networks for ordinary differential equations (34B45)

Related Items (4)

Computational networks and systems -- homogenization of self-adjoint differential operators in variational form on periodic networks and micro-architectured systems ⋮ Bridging the gap between variational homogenization results and two-scale asymptotic averaging techniques on periodic network structures ⋮ A reconstruction of object properties with significant uncertainties ⋮ Homogenization of optimal control problems on curvilinear networks with a periodic microstructure -- results on \(S\)-homogenization and \(\Gamma\)-convergence

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