An unfitted Hybrid High-Order method for the Stokes interface problem

Erik Burman (1) , Guillaume Delay (2, 3, 4) , Alexandre Ern (3, 4)

1 UCL London - Department of Mathematics
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
4 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms

We design and analyze a hybrid high-order (HHO) method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.

Domaines: Analyse numérique [math.NA]

Erik Burman, Guillaume Delay, Alexandre Ern. An unfitted Hybrid High-Order method for the Stokes interface problem. IMA Journal of Numerical Analysis, 2021, 41 (4), pp.2362-2387. ⟨10.1093/imanum/draa059⟩. ⟨hal-02519896v4⟩