@Article{IJNAM-12-3,
author = {},
title = {A Finite Element Dual Singular Function Method to Solve the Stokes Equations Including Corner Singularities},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2015},
volume = {12},
number = {3},
pages = {516--535},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/2015-IJNAM-500},
url = {https://global-sci.com/article/83305/a-finite-element-dual-singular-function-method-to-solve-the-stokes-equations-including-corner-singularities}
}