A cut finite element method with boundary value correction for the incompressible Stokes' equations
This work provides a practical and accurate numerical method for solving Stokes flow on complex curved geometries, which is important for computational fluid dynamics applications.
The paper develops a cut finite element method for the incompressible Stokes equations on curved domains, using a piecewise affine discrete domain and Nitsche's method for Dirichlet conditions, with boundary value correction to account for the curved physical boundary. Numerical results demonstrate optimal convergence rates.
We design a cut finite element method for the incompressible Stokes equations on curved domains. The cut finite element method allows for the domain boundary to cut through the elements of the computational mesh in a very general fashion. To further facilitate the implementation we propose to use a piecewise affine discrete domain even if the physical domain has curved boundary. Dirichlet boundary conditions are imposed using Nitsche's method on the discrete boundary and the effect of the curved physical boundary is accounted for using the boundary value correction technique introduced for cut finite element methods in Burman, Hansbo, Larson, 'A cut finite element method with boundary value correction', Math. Comp. 87(310):633--657, 2018.