# A Hybrid High-Order method for the convective Cahn-Hilliard problem in mixed form

## TL;DR

This paper introduces a new Hybrid High-Order numerical method for solving the convective Cahn-Hilliard problem, capable of handling complex meshes and demonstrating robustness across different flow regimes.

## Contribution

It develops a flexible, high-order hybrid method applicable in 2D and 3D with general meshes, advancing numerical solutions for convection-influenced phase separation.

## Key findings

- Method is valid in 2D and 3D
- Supports arbitrary approximation orders
- Shows robustness with respect to Péclet number

## Abstract

We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing polyhedral elements and nonmatching interfaces. An extensive numerical validation is presented, which shows robustness with respect to the P\'eclet number.