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

TL;DR

This paper introduces a micromorphic-based finite element method that stabilizes reaction-convection-diffusion equations by gradient enhancement, improving accuracy and stability for complex problems with varying reactivity and convection.

Contribution

It presents a novel gradient-enhanced approach with proven well-posedness and error estimates, demonstrating superior stability and accuracy over traditional methods.

Findings

High accuracy in 1D and 2D numerical examples

Enhanced stability for complex reaction-convection scenarios

Effective handling of varying reactivity and convection levels

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.