A cut-cell Hybrid High-Order method for elliptic problems with curved boundaries

Erik Burman (1) , Alexandre Ern (2, 3)

1 UCL - University College of London [London]
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms

We design a Hybrid High-Order method for elliptic problems on curved domains. The method uses a cut cell technique for the representation of the curved boundary and imposes Dirichlet boundary conditions using Nitsche's method. The physical boundary can cut through the cells in a very general fashion and the method leads to optimal error estimates in the H1-norm.

Domaines: Analyse numérique [math.NA]

Erik Burman, Alexandre Ern. A cut-cell Hybrid High-Order method for elliptic problems with curved boundaries. ENUMATH 2017, Sep 2017, Bergen, Norway. ⟨10.1007/978-3-319-96415-7_14⟩. ⟨hal-01653685v2⟩