A study of mimetic and finite difference methods for the static diffusion equation

Abstract

Two second-order finite difference methods in a staggered mesh to solve the static diffusion equation are proposed in this article. These methods were compared with a standard finite difference method and with two numerical schemes naturally established in staggered grids: mimetic method and conservative method. Also, mimetic discretization is presented in a formal manner. The methods were tested using different configurations, including boundary layers and heterogeneous media. The study shows that the two proposed finite difference methods produce numerical solutions that are comparable to those given by mimetic methods, in terms of rates of convergence and magnitude of the approximation error.