Soheil Firooz ; B. Daya Reddy ; Paul Steinmann - A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems

jtcam:15788 - Journal of Theoretical, Computational and Applied Mechanics, October 5, 2025 - https://doi.org/10.46298/jtcam.15788
A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problemsArticle

Authors: Soheil Firooz ORCID; B. Daya Reddy ORCID; Paul Steinmann ORCID

    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.

    pages: 1-17

    https://doi.org/10.46298/jtcam.15788
    Source: arXiv.org:2506.01873
    Published on: October 5, 2025
    Accepted on: August 9, 2025
    Submitted on: June 3, 2025
    Keywords: Mathematical Physics

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    Soheil Firooz, B. Daya Reddy, Paul Steinmann, Benoît Panicaud, Samuel Forest. Open Review of "A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems". 2025. ⟨hal-05279377⟩

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