A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems
Abstract
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.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Advanced Mathematical Modeling in Engineering
Numerical methods in engineering
Publication details
- Journal / source
- Archive of Applied Mechanics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 96
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN