Numerical resolution of diffusion equations using a weakly monotone finite volume method on tetrahedral meshes

In this paper, we propose and extend the weakly monotone finite volume (WMFV) technique to discretize parabolic equations in 3D on tetrahedral meshes with anisotropy.The key idea is to introduce a nonlinear correction coefficient based on a centered approximation of the mobility function.This approach eliminates anti-diffusive fluxes, leading to a more accurate, robust, and efficient solver.Numerical validations are conducted to emphasize the accuracy and the stability of our method.Comparisons to the standard control volume finite element method and to its positive version are also provided.