A Conservative Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations

In this paper we develop a cell-centered finite volume scheme which preserves the maximum principle for diffusion equations. Two combination are consisted in the construction, i.e., a linear combination of two one-side normal fluxes and a nonlinear combination of two one-side tangential fluxes. It is proved that this nonlinear scheme satisfies discrete maximum principle (DMP). Moreover, the existence of a solution of the nonlinear finite volume scheme is proved without imposing the coercivity assumption on the discrete fluxes. Numerical results are presented to show the conservation, accuracy and positivity of the scheme.