NDLI: A note on a finite element method dealing with corner singularities

Content Provider	Springer Nature Link
Author	Kim, Seokchan Woo, Gyungsoo Park, Taehoon
Copyright Year	2000
Abstract	Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7]. They use the well-known fact that the solution of such problem has a singular representation, deduce a well-posed new variational problem for regular part of solution and an extraction formula for the so-called stress intensity factor using two cut-off functions.They use Fredholm alternative and Gårding’s inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for meshh theoretically, although the numerical experiments shows the convergence for every reasonable size ofh. In this paper we show that the method converges for everyh with reasonable size by imposing a restriction to the support of the extra cut-off function without using Gårding’s inequality. We also give error analysis with similar results.
Starting Page	373
Ending Page	386
Page Count	14
File Format	PDF
ISSN	12260061
Journal	Journal of Applied Mathematics and Computing
Volume Number	7
Issue Number	2
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	2000-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Spectral, collocation and related methods Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing
Content Type	Text
Resource Type	Article

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