L.E.S. Queiroz, M.R.A. Souza, F.R.L. Contreras, P.R.M. Lyra and D.K.E. de Carvalho
In this paper, we consider a nonlinear finite volume method to solve the steady-state diffusion equation in heterogeneous and anisotropic media. In its original form, the scheme is monotone, but unable to reproduce piecewise linear solutions exactly. To recover this interesting feature, we use two different interpolation strategies. In this case, even though we cannot prove monotonicity, we present numerical evidences that the combined method has an improved behavior, producing second order accurate solutions for heterogeneous and anisotropic media.