In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides great flexibility in mesh design and adaptation, and can accommodate large variations of both the displacement and damage variables thanks to the use of fully discontinuous spaces. The resolution of the corresponding algebraic problem is based on a staggered time stepping scheme which takes advantage of static condensation for each subproblem. We provide extensive numerical validation of the method on classical two-dimensional fracture propagation problems, including a comparison with a more standard finite element scheme.
@article{arxiv.2511.15345,
title = {A Hybrid-High Order method for fracture modelling},
author = {Alessandra Crippa and Julien Coatléven and Daniele A. Di Pietro and Nicolas Guy and Yousef Soleiman},
journal= {arXiv preprint arXiv:2511.15345},
year = {2025}
}