A new tailored finite point method for strongly anisotropic diffusion equation on misaligned grids

This paper presents a new tailored finite point method (TFPM) for the strongly anisotropic diffusion equation on Cartesian coordinates. The novelty is that the scheme is constructed by using the interface conditions for each cell. Several numerical experiments are presented to show the performance of this new scheme. Numerically, the method can not only achieve good accuracy, but also sharply capture internal layers. (C) 2019 Elsevier Inc. All rights reserved.