A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems

Firooz S, Reddy BD, Steinmann P (2026)

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

DOI: 10.48550/arXiv.2506.14800

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.

Authors with CRIS profile

Soheil Firooz Lehrstuhl für Technische Mechanik (LTM) Paul Steinmann Lehrstuhl für Technische Mechanik (LTM)

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)

How to cite

APA:

Firooz, S., Reddy, B.D., & Steinmann, P. (2026). A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems. (Unpublished, Submitted).

MLA:

Firooz, Soheil, B. Daya Reddy, and Paul Steinmann. A micromorphic-based artificial diffusion method for stabilized finite element approximation of convection-diffusion problems. Unpublished, Submitted. 2026.

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