A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems

Firooz S, Reddy BD, Steinmann P (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Theoretical, Computational and Applied Mechanics Episciences

Article Number: 15788

DOI: 10.46298/jtcam.15788

Abstract

We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the coupled-field approach is established, together with an error estimate. Through a set of 1D and 2D numerical examples the high accuracy and enhanced stability of the approach in approximating solutions associated with complex problems is demonstrated, for situations of varying reactivity and convection.

Authors with CRIS profile

Soheil Firooz Lehrstuhl für Technische Mechanik (LTM) Paul Steinmann

Additional Organisation(s)

Sonderforschungsbereich 1540/1 - Erforschung der Mechanik des Gehirns (EBM): Verständnis, Engineering und Nutzung mechanischer Eigenschaften und Signale in der Entwicklung, Physiologie und Pathologie des zentralen Nervensystems

Involved external institutions

University of Cape Town (UCT) ZA South Africa (ZA) University of Glasgow GB United Kingdom (GB)

How to cite

APA:

Firooz, S., Reddy, B.D., & Steinmann, P. (2025). A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems. Journal of Theoretical, Computational and Applied Mechanics. https://doi.org/10.46298/jtcam.15788

MLA:

Firooz, Soheil, B. Daya Reddy, and Paul Steinmann. "A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems." Journal of Theoretical, Computational and Applied Mechanics (2025).

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