TY - JOUR
T1 - A Finite Element Dual Singular Function Method to Solve the Stokes Equations Including Corner Singularities
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 516
EP - 535
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/500.html
KW - Stokes equations, dual singular function method, corner singularity, incompressible fluids.
AB - <p style="text-align: justify;">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 $\rm{H}^1(Ω)$ and pressure in $L^2(Ω)$, but we are able to prove only $O(h^{1+\lambda})$ error bounds for
velocity in $\rm{L}^2(\Omega)$ and stress intensity factor, where $\lambda$ is the eigenvalue (solution of (4)). However,
we get optimal accuracy results in numerical experiments.</p>