A cut finite element method with boundary value correction for the incompressible Stokes' equations

TL;DR

This paper introduces a cut finite element method with boundary value correction for solving the incompressible Stokes equations on curved domains, enabling flexible boundary handling and improved implementation.

Contribution

It presents a novel cut finite element approach that uses boundary value correction and affine discrete domains for better accuracy on curved boundaries.

Findings

Allows boundary cuts through elements in a general manner

Uses Nitsche's method for boundary conditions

Incorporates boundary value correction for curved boundaries

Abstract

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.