Lower Bounds for the Error in Nitsche’s Method for the Navier–Stokes Equations With Slip Boundary Conditions

Ingeborg Gjerde; L. Ridgway Scott. 1 July, 2021.
Communicated by L. Ridgway Scott.


We investigate lower bounds for the error in Nitsche’s Method to implement slip boundary conditions for flow problems in domains with curved boundaries. We study approximations of the normal and tangent vectors when using a polygonal approximation of the domain. For both approaches, we give lower bounds for the error that give an upper bound on the best convergence rate that can be achieved for a polygonal approximation of a curved boundary. Our results support the idea that extra mesh refinement near a curved boundary can mitigate the polygonal domain approximation error.

Original Document

The original document is available in PDF (uploaded 1 July, 2021 by L. Ridgway Scott).