An error analysis for the corner singularity expansion of a compressible Stokes system on a non-convex polygon

Abstract

It is known that the velocity vector for compressible Navier-Stokes flows with non-zero boundary conditions can be decomposed into a singular part and its regular one near each non-convex vertex of bounded polygonal domains. The singular part is a multiplication of the corner singularity (of the Laplace type) and the stress intensity factor. In this paper we consider a finite element scheme approximating the regular part and the stress intensity factor, show its unique existence of the discrete solution and derive an (nearly) optimal error estimate. Some numerical examples confirming these results are given.