How to integrate FCT in FEniCSx to reduce numerical oscillations in convection-diffusion equations

Hello everyone,

I am currently using FEniCSx to solve convection-diffusion equations and am encountering numerical oscillations in my fluid dynamics simulations, which I understand is often due to convection dominance. I am considering using the Flux-Corrected Transport (FCT) method to improve my numerical solutions.

I already have a framework based on the standard Galerkin FEM method, but I am unsure how to implement FCT in FEniCSx. I aim to reduce numerical oscillations and enhance the accuracy of my simulations. I would greatly appreciate any example codes or advice from experienced developers in the community.

Thank you for your help!