The unfitted HHO method for the Stokes problem on curved domains

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

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

We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and a priori estimates with optimal convergence rates. Moreover, we provide numerical simulations that corroborate the theoretical convergence rates. A cell-agglomeration procedure is used to prevent the appearance of small cut cells.

Domaines: Analyse numérique [math.NA]

Erik Burman, Guillaume Delay, Alexandre Ern. The unfitted HHO method for the Stokes problem on curved domains. ENUMATH - European Numerical Mathematics and Advanced Applications Conference 2019, Sep 2019, Egmond an Zee, Netherlands. ⟨hal-02438622⟩