Volume 12, Issue 3
A Finite Element Dual Singular Function Method to solve the Stokes Equations Including Corner Singularities

Jae-Hong Pyo

Int. J. Numer. Anal. Mod., 12 (2015), pp. 516-535

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  • 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 H¹(Ω ) and pressure in L²(Ω ), but we are able to prove only O(h^{+λ) error bounds for velocity in L²( Ω) and stress intensity factor, where λ is the eigenvalue (solution of (4)). However, we get optimal accuracy results in numerical experiments.

  • History

Published online: 2015-12

  • AMS Subject Headings

65M12, 65M15, 76D05

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