Compressible Navier-Stokes equations in a bounded domain with inflow boundary condition
SIAM Journal on Mathematical Analysis
Overcoming Corner Singularities Using Multigrid Methods
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities
SIAM Journal on Numerical Analysis
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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.