A FINITE ELEMENT DUAL SINGULAR FUNCTION METHOD TO SOLVE THE STOKES EQUATIONS INCLUDING CORNER SINGULARITIES

摘要

The finite element dual singular function method [FE-DSFM] has been constructed and analyzed accuracy by Z. Cai and S. Kim to solve the Laplace equation on a polygonal domain with one reentrant corner. In this paper, we impose FE-DSFM to solve the Stokes equations via the mixed finite element method. To do this, we compute the singular and the dual singular functions analytically at a non-convex corner. We prove well-posedness by using the contraction mapping theorem and then estimate errors of the algorithm. We obtain optimal accuracy O(h) for velocity in H-1(Omega) and pressure in L-2(Omega), but we are able to prove only O(h(1+lambda)) error bounds for velocity in L-2(Omega) and stress intensity factor, where lambda is the eigenvalue (solution of (4)). However, we get optimal accuracy results in numerical experiments.