Robustness of finite element simulations in densely packed random particle composites
Daniel Peterseim, ,Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin · Networks and Heterogeneous Media · 2012
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.