Two uniform tailored finite point method for strongly anisotropic and discontinuous diffusivity

Abstract

The paper presents two Tailored Finite Point method (TFPM) for the diffusion equations, which is valid for the strongly anisotropic tensor diffusivity and interface layers. The first scheme uses the value as well as their derivatives at the grid points to construct the five point scheme for the heterogeneous rotating anisotropy. The second scheme is based on the interface conditions to construct the four point scheme for each cell, which gives rise to desirable internal layers and discontinuous diffusivity conditions. Numerically, both methods can achieve uniform convergence, even when there exhibit interface layers. Numerical experiments are presented to show the performance of the proposed two different schemes.