Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation
Firooz S, Reddy BD, Zaburdaev V, Steinmann P (2024)
Publication Type: Journal article
Publication year: 2024
Journal
Book Volume: 419
Pages Range: 116649
Article Number: 116649
DOI: 10.1016/j.cma.2023.116649
Abstract
We develop and implement finite element approximations for the coupled problem of cellular aggregate formation. The equation governing evolution of cell density is convective in nature, necessitating a modification of standard approaches to circumvent the instabilities associated with standard finite element approximations. To this end, a novel mean zero artificial diffusion approach is proposed, in which the classical artificial diffusion term is replaced by one that is orthogonal to its projection on to continuous functions. The resulting approach for the convective equation is shown to be well-posed. A range of numerical results illustrate the stability and accuracy of the new approach, and its behaviour in comparison with an alternative approach using Taylor–Hood elements. The results also provide insights into the behaviour of cellular aggregates in the context of the model studied here.
Authors with CRIS profile
Soheil Firooz
Lehrstuhl für Technische Mechanik (LTM)
Vasily Zaburdaev
Lehrstuhl für Mathematik in den Lebenswissenschaften
Paul Steinmann
Lehrstuhl für Technische Mechanik (LTM)
Involved external institutions
South Africa (ZA)How to cite
APA:
Firooz, S., Reddy, B.D., Zaburdaev, V., & Steinmann, P. (2024). Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation. Computer Methods in Applied Mechanics and Engineering, 419, 116649. https://doi.org/10.1016/j.cma.2023.116649
MLA:
Firooz, Soheil, et al. "Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation." Computer Methods in Applied Mechanics and Engineering 419 (2024): 116649.
BibTeX: Download