Hybrid high-order method for singularly perturbed fourth-order problems on curved domains

Zhaonan Dong (1, 2) , Alexandre Ern (1, 2)

1 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourthorder PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and a scaling of the weighting parameter in the stabilization operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, including the zero value for which a second-order elliptic problem is recovered. Numerical experiments illustrate the theoretical analysis.

Mots clés: Stability; Curved domains; Polytopal meshes; Robustness; Hybrid high-order method; Singularly perturbed fourth-order PDEs; Error analysis

Domaines: Analyse numérique [math.NA]

Zhaonan Dong, Alexandre Ern. Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (6), pp.3091-3114. ⟨10.1051/m2an/2021081⟩. ⟨hal-03322267v2⟩