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

2025/06/02 by Soheil Firooz, Firooz, Soheil, B.D. Reddy +3
Engineering · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities

paper · pdf · doi:10.48550/arxiv.2506.01873

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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