An analysis on the penalty and Nitsche's methods for the Stokes–Darcy system with a curved interface

Guanyu Zhou*, Takahito Kashiwabara, Issei Oikawa, Eric Chung, Ming-Cheng Shiue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze the penalty and Nitsche's methods, in the continuous and discrete senses, for the Stokes–Darcy system with a curved interface. In the continuous sense, we prove the stability and optimal convergence for the penalty approach. In discretization, the curved interface is approximated by polygonal surface. We propose the discontinuous Galerkin (DG) penalty/Nitsche schemes, and establish the stability and error analysis taking the domain perturbation into account. To obtain sharp estimates on the pressure constant and the inf-sup condition involving the integration on the interface, we study the broken H1/2 norm of the DG element, and prove a DG version of the reversed trace operator.

Original languageEnglish
Pages (from-to)83-118
Number of pages36
JournalApplied Numerical Mathematics
Volume165
DOIs
StatePublished - Jul 2021

Keywords

  • Discontinuous Galerkin method
  • Nitsche's method
  • Penalty method
  • Stokes–Darcy system

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