Singular Finite Element Method For Stokes Equation With Corner Singularity

In this paper, we combine singular finite element method and penalty parametermethod for the two-dimensional Stokes equation with corner singularity. The main proce-dure includes two steps: Firstly, under polar coordinates, we discretize the Stokes equationonly in theθ-direction, and use the penalty parameter method to get the semi-discrete finiteelement solution, which can be reduced to solve an algebraic eigenvalue problem. Using theeigenvalues and eigenvectors, we can obtain the approximate singularity expansion of theoriginal problem at the corner. Secondly, we construct the singular finite element space bycombining the standard basis functions with the singular basis functions chosed from theapproximate singularity expansion. Then we solve the Stokes equation problem in the sin-gular finite element spaces. The numerical example shows that this method is e?ective.