A modified dynamic diffusion finite element method with optimal convergence rate for convection-diffusion-reaction equations
Numerical Analysis
2025-03-11 v1 Numerical Analysis
Abstract
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We prove existence and, under an assumption of small mesh size, uniqueness of the discrete solution, and derive the optimal first order convergence rate of the approximation error in the energy norm plus a dissipation term. Numerical examples are provided to verify the theoretical analysis.
Cite
@article{arxiv.2503.06555,
title = {A modified dynamic diffusion finite element method with optimal convergence rate for convection-diffusion-reaction equations},
author = {Shaohong Du and Qianqian Hou and Xiaoping Xie},
journal= {arXiv preprint arXiv:2503.06555},
year = {2025}
}