Networks and Heterogeneous Media (NHM)

Robustness of finite element simulations in densely packed random particle composites

Pages: 113 - 126, Volume 7, Issue 1, March 2012      doi:10.3934/nhm.2012.7.113

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Daniel Peterseim - Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany (email)

Abstract: This paper presents some weighted $H^2$-regularity estimates for a model Poisson problem with discontinuous coefficient at high contrast. The coefficient represents a random particle reinforced composite material, i.e., perfectly conducting circular particles are randomly distributed in some background material with low conductivity. Based on these regularity results we study the percolation of thermal conductivity of the material as the volume fraction of the particles is close to the jammed state. We prove that the characteristic percolation behavior of the material is well captured by standard conforming finite element models.

Keywords:  Perforated domain, thickness of a domain, finite element method, high contrast, percolation, phase transition.
Mathematics Subject Classification:  Primary: 35B65, 65N15; Secondary: 65N30, 74Q20.

Received: July 2011;      Revised: October 2011;      Available Online: February 2012.