A homogenization result for planar, polygonal networks

DOI10.1051/m2an/1991250404831zbMath0737.35126OpenAlexW2468414760MaRDI QIDQ3978386

Michael S. Vogelius

Publication date: 25 June 1992

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193637

zbMATH Keywords

homogenizationnetworks

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Second-order elliptic equations (35J15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (14)

Computational networks and systems -- homogenization of self-adjoint differential operators in variational form on periodic networks and micro-architectured systems ⋮ HOMOGENIZATION OF ELECTRICAL NETWORKS INCLUDING VOLTAGE-TO-VOLTAGE AMPLIFIERS ⋮ Numerical homogenization: survey, new results, and perspectives ⋮ Internal variables and fine-scale oscillations in micromagnetics ⋮ Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure -- efficient solution strategies based on homogenization theory ⋮ Mechanics of materials with periodic truss or frame micro-structures ⋮ Bridging the gap between variational homogenization results and two-scale asymptotic averaging techniques on periodic network structures ⋮ Spectral measure and approximation of homogenized coefficients ⋮ Computational networks and systems – homogenization of variational problems on micro-architectured networks and devices ⋮ Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality ⋮ Homogenization of optimal control problems on curvilinear networks with a periodic microstructure -- results on \(S\)-homogenization and \(\Gamma\)-convergence ⋮ Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation ⋮ Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs ⋮ REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS

Cites Work

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• The diffusion limit for reversible jump processes on \(Z^ m\) with ergodic random bond conductivities
• The extremal length of a network
• \(\Gamma\)-limits of integral functionals
• \(G\)-closure of a set of anisotropically conducting media in the two-dimensional case
• Topology of series-parallel networks
• Estimating Dirichlet's integral and electrical conductance for systems which are not self-adjoint
• Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
• Interior Estimates for Ritz-Galerkin Methods
• Some remarks on the optimal design of periodically reinforced structures
• Triangular Elements in the Finite Element Method

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