Two-dimensional site percolation and conduction

The authors introduce the finite-element method for the effective conductivity of two-dimensional composite materials. For the problem of two-dimensional percolation and conduction they use three kinds of composite material with regular cell structure and compute an upper and a lower bound on the effective conductivity of the materials by the finite-element method. The three models can be related to site percolation problems, and the relation between the computed bounds and two kinds of percolation problems (current percolation and field percolation) is made clear.