An error analysis of the finite element method of the Stokes equations with parameter based on the singular function expansion

Abstract In this paper, we introduce a mixed finite element method of the Stokes system with parameter on a non‐convex polygon. This model problem is considered in the time‐discretization of the unstationary Stokes equations, and it is mentioned in Kweon's study that the velocity field and the pressure function are composed of singular parts and smoother remainders due to the corner singularities of the solution near each re‐entrant corner. We propose a stable numerical scheme to approximate the coefficients in singular part and the regular part of solution, based on the extraction formulae of the coefficients in singular part. Furthermore, to show the reliability of the proposed method, we derive the absolute error estimates of the approximations of coefficients, and the and error estimates of the finite element solution corresponding to the regular part.