A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems - Firooz, Soheil; Reddy, B. Daya; Steinmann, Paul (2026)
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 problem
https://cris.fau.de/converis/publicweb/Publication/352803579