no. 6
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 3091-3114

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.

DOI : 10.1051/m2an/2021081
Classification : 65N15, 65N30, 74K20
Keywords: Singularly perturbed fourth-order PDEs, hybrid high-order method, robustness, stability, error analysis, polytopal meshes, curved domains 
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     author = {Dong, Zhaonan and Ern, Alexandre},
     title = {Hybrid high-order method for singularly perturbed fourth-order problems on curved domains},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {3091--3114},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     number = {6},
     doi = {10.1051/m2an/2021081},
     zbl = {1490.65269},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2021081/}
}
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Dong, Zhaonan; Ern, Alexandre. Hybrid high-order method for singularly perturbed fourth-order problems on curved domains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 3091-3114. doi: 10.1051/m2an/2021081

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