Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ERROR ESTIMATION OVER THE POLYGONAL DOMAINS BY THE FINITE ELEMENT METHOD

  • Kim, Chang-Geun (Department of Mathematics, Research Institute of Basic Science, Kwangwoon University)
  • Published : 2002.12.01

⟨ Previous Next ⟩

Abstract

For second order linear elliptic problems over smooth domains, it is well known that the rate of convergence of the error in the $L_2$norm is one order higher than that in the $H^1$norm. For polygonal domains with reentrant corners, it has been shown in [15] that this extra order cannot be fully recovered when the h-version is used. We present theoretical and computational examples showing the sharpness of our results.

Keywords

References

  1. Computer Meth. in Appl. Mech. and Eng. v.45 Finite element methods: Principles for their selection D.N.Arnold;I.Babuska;J.Osborn
  2. Impact of Computing in Science and Engineering v.1 Implementation of non-homogeneous Dirichlet boundary conditions in the p-version of the finite element method I.Babuska;B.Guo;M.Suri
  3. SIAM J. Numer. Anal. v.24 The optimal convergence rate of the p-version of the finite element method I.Babuska;M.Suri
  4. Computer Meth. in Appl. Mech. and Eng. v.80 The p- and h - p versions of the finite element method. An Overview I.Babuska;M.Suri.
  5. Applicable Analysis Polynomial approximation of some singular functions C.Bernardi;Y.Maday
  6. Finite Element Hanbook Functional spaces F.Brezzi;G.Gilardi;H.Kardestuncer(ed.)
  7. Math. Comp. v.38 Approximation results for orthogonal polynomials in Sobolev spaces C.Canuto;A.Quarteroni
  8. Finite Element Handbook Finite Element Approximation Theory P.G.Ciarlet;H.Kardestuncer(ed.)
  9. SIAM J.Numer. Anal. v.21 The approximation theory for the p-version of the finite element method M.R.Dorr
  10. SIAM J. Numer. Anal. v.23 Some error estimates for the p-version of the finite element method K.Eriksson
  11. Elliptic Problems in Nonsmooth Domains P.Grisvard
  12. Numerische Mathematik On computing the pressure by the p version of the finite element method for Stokes problem S.Jensen
  13. RAIRO Math. Mod. Numer. Anal. v.24 The p-version of the finite element method for elliptic equations of order 2ℓ M.Suri
  14. Finite element analysis B.Szabo;I.Babuska
  15. Math. Comp. v.42 On the sharpness of certain estimates for H¹ projections into finite element spaces: influence of a reentrant corner L.B.Wahlbin