Finite element methods for elliptic partial differential equations on non-convex polygonal domains

DoctorIn this dissertation, we study the Poisson problem with homogeneous boundary datum in a finite polyhedral cylinder with a non-convex edge. Applying the Fourier sine series to the equation along the edge and by a corner singularity expansion for the Poisson problem with parameter, we defne the edge flux coefficient and the regular part of the solution on the polyhedral cylinder. We present the Fourier-finite element method for approximating the edge flux coefficient and the regular part. We show the stability and derive error estimates. Some numerical simulations are presented. Furthermore, we give a numerical simulation for a compressible viscous Stokes system on non-convex polygonal domains and confirm the theoretical results by the numerical examples