Volume 55, Number 6, November-December 2021
|Page(s)||3091 - 3114|
|Published online||24 December 2021|
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains
Inria, 2 rue Simone Iff, 75589 Paris, France
2 CERMICS, Ecole des Ponts, 77455 Marne-la-Vallée, France
* Corresponding author: firstname.lastname@example.org
Accepted: 8 December 2021
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order 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.
Mathematics Subject Classification: 65N15 / 65N30 / 74K20
Key words: Singularly perturbed fourth-order PDEs / hybrid high-order method / robustness / stability / error analysis / polytopal meshes / curved domains
© The authors. Published by EDP Sciences, SMAI 2021
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