The Crouzeix–Raviart element for the Stokes equations with the slip boundary condition on a curved boundary

Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis

“…Remark 3.1 In this work, we do not address the situation with curved boundary, but we refer the interested readers to the work in [25,26].…”

“…The later being defined on the flow domain Ω, and the constitutive relation bringing together the Cauchy stress tensor and the symmetric part of the velocity gradient. Finally, we observe that (1.7) is a generalisation of the Navier's slip boundary condition, which is an active research direction (see [22,23,24,25,26,27]).…”

The penalty method for the boundary condition of the Darcy system

“…But such transformation could be unavailable or nontrivial to construct. The Lagrange multiplier method [21,22] is a successful method, which implements u u u h • n n n h = g in the weak sense. But it introduces an additional new unknown (called the Lagrange multiplier) in a finite element space defined on the mesh of the boundary (also an additional equation as well), which increases the computational cost.…”