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Conference Papers Year : 2021

Hybrid high-order methods for elliptic PDEs on curved and complicated domains

Abstract

We introduce a variant of the hybrid high-order method (HHO) employing Nitsche’s boundary penalty techniques for the Poisson problem on the curved and complicated Lipschitz domain. The proposed method has two advantages: Firstly, there are no face unknowns introduced on the boundary of the domain, which avoids the computation of the parameterized mapping for the face unknowns on the curved domain boundary. Secondly, using Nitsche’s boundary penalty techniques for weakly imposing Dirichlet boundary conditions one can obtain the stability and optimal error estimate independent of the number and measure of faces on the domain boundary. Finally, a numerical experiment is presented in this chapter to confirm the theoretical results.
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Dates and versions

hal-03476090 , version 1 (12-12-2021)
hal-03476090 , version 2 (09-05-2022)

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  • HAL Id : hal-03476090 , version 2

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Zhaonan Dong, Zuodong Wang. Hybrid high-order methods for elliptic PDEs on curved and complicated domains. 13th ICOSAHOM 2020/2021 Conference Proceeding, Jul 2021, Vienna, Austria. ⟨hal-03476090v2⟩
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