A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems
Numerical Analysis
2025-06-19 v1 Numerical Analysis
Mathematical Physics
math.MP
Abstract
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary variable, which is related to the gradient of the field of interest, and which leads to a coupled problem. Conditions for well-posedness of the resulting formulation are established. We carry out a comprehensive numerical study to compare the proposed methodology against some well-established approaches in one- and two-dimensional settings. The proposed method outperforms established approaches in general in approximating accurately the solutions to pertinent and challenging problems.
Cite
@article{arxiv.2506.14800,
title = {A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems},
author = {Soheil Firooz and B. Daya Reddy and Paul Steinmann},
journal= {arXiv preprint arXiv:2506.14800},
year = {2025}
}