AbstractThe diffusion of electric charge on a thin-film dielectric is described by an initial-boundary-value problem for a parabolic partial differential equation on a planar region. Consider the situation where conductivity on a given subregion increases to large values and the corresponding limiting problem has the total capacitance of that subregion all concentrated on the boundary of the complementary region. As the conductivity increases, the convergence of the solutions to that of the limiting problem is established, and convergence rates are obtained. The additional effect of deleting this concentrated capacitance is also estimated.