We construct a nonlinear finite volume (FV) scheme for diffusion equation on star-shaped polygonal meshes and prove that the scheme is monotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients.Expand

We construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle.Expand

A nonoverlapping domain decomposition method for some time-dependent convection-diffusion equations is presented. It combines predictor-corrector technique, modified upwind differences with… Expand

We construct a monotone finite volume scheme on distorted meshes for multimaterial, nonequilibrium radiation diffusion problems, which are described by the coupled radiation diffusion and material conduction equations.Expand

We employ the so-called linearity preserving method, which requires that a difference scheme should be exact on linear solutions, to derive a nine-point difference scheme for the numerical solution of diffusion equation on the structured quadrilateral meshes.Expand