A monotone $Q^1$ finite element method for anisotropic elliptic equations
Numerical Analysis
2024-07-30 v2 Numerical Analysis
Abstract
We construct a monotone continuous finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle. Convergence of the new scheme is rigorously proven. On quadrilateral meshes, the matrix coefficient conditions translate into specific mesh constraints.
Cite
@article{arxiv.2310.16274,
title = {A monotone $Q^1$ finite element method for anisotropic elliptic equations},
author = {Hao Li and Xiangxiong Zhang},
journal= {arXiv preprint arXiv:2310.16274},
year = {2024}
}