Analysis of a New NFV Scheme Preserving DMP for Two-Dimensional Sub-diffusion Equation on Distorted Meshes

In this paper, we describe a new nonlinear finite-volume scheme that preserves the discrete maximum principle (DMP) for the two-dimensional sub-diffusion equation on distorted meshes. One distinguishing feature of our method is its ability to uphold the DMP for the anisotropic sub-diffusion problems, thereby ensuring the absence of spurious oscillations in numerical solutions and maintaining the physical bounds of various quantities, such as concentration, temperature, and density. Notably, our scheme offers the advantage of being applicable to distorted meshes without stringent constraints. Numerical results demonstrate that our scheme successfully preserves maximum principle on various randomly distorted meshes.