A penalty method for the time-dependent Stokes problem with the slip boundary condition
 
and its finite element approximation

Zhou, Guanyu; Kashiwabara, Takahito; Oikawa, Issei

doi:10.21136/am.2017.0328-16

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2019

2024

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Cited by 6 publications

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“…In the present work, we continue the previous works for the Stokes and Navier-Stokes' cases [23,24,25], and study the penalty approach for the Darcy system. The idea is to add the penalty term 1 ε Γ (u u u ε − g) • n n nv v v • n n n ds to the variational equation with a tiny positive penalty parameter ε.…”

Section: Introductionmentioning

confidence: 79%

The penalty method for the boundary condition of the Darcy system

2022

J. Appl. Numer. Optim.

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We propose a penalty method to approximate the boundary condition of the Darcy system. For the penalty variational problem, we establish the well-posedness theorem and prove the optimal error estimates of the penalty in the continuous sense. Moreover, we apply the finite element method using RT0/P0 element to discretize the penalty variational problem. The convergence rate depending on both the penalty parameter and mesh size, as well as the applicability of the discrete scheme, are investigated through several numerical experiments on the cases with smooth/non-smooth and convex/non-convex domains.

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