A finite element method for Stokes equation using discrete singularity expansion

The numerical method presented in this paper for Stokes equation with corner singularity includes mainly two steps. Firstly, we solve a simple eigenvalue problem, which is one dimension less than the original problem, to obtain the discrete expansion of the singularity near the corner. Secondly, we combine the approximation of the singularity and standard finite element basis functions to construct special finite element spaces, and solve the original problem in the special spaces on a conventional mesh. The numerical examples show the effectiveness of this method.