A Finite Element Dual Singular Function Method to Solve the Stokes Equations Including Corner Singularities
Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 3 : pp. 516–535
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-500
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 3 : pp. 516–535
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stokes equations dual singular function method corner singularity incompressible fluids.