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arXiv · 2506.01873

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

Soheil Firooz·B. Daya Reddy·Paul Steinmann
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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.

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Soheil Firooz, B. Daya Reddy, Paul Steinmann. 2025-06-02. A gradient-enhanced approach for stable finite element approximations of reaction-convection-diffusion problems. https://doi.org/10.46298/jtcam.15788

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