Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations

@article{Levine1985SuperconvergentRO,
  title={Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations},
  author={N. Levine},
  journal={Ima Journal of Numerical Analysis},
  year={1985},
  volume={5},
  pages={407-427}
}
  • N. Levine
  • Published 1 October 1985
  • Mathematics
  • Ima Journal of Numerical Analysis
On justifie l'utilisation d'un schema simple pour determiner les gradients a partir de l'approximation a elements finis triangulaires lineaire par morceaux de la solution d'un probleme elliptique du second ordre. Le gradient obtenu est une estimation superconvergente du vrai gradient 
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References

SHOWING 1-10 OF 23 REFERENCES
Superconvergence of the gradient of finite element solutions
Super convergence of the gradient of approximate solutions to second order elhptic équations is analysed and justified for a large ciass of curved isoparametric quadrilatéral éléments Résumé — On…
Superconvergence and reduced integration in the finite element method
The finite elements considered in this paper are those of the Serendipity family of curved isoparametric elements. There is given a detailed analysis of a superconvergence phenomenon for the gradient…
Some superconvergence results in the finite element method
Superconvergence of the gradient of finite element solutions of 2nd order problems is proved at Gaussian points when finite element spaces constructed by means of polynomials of the Serendipity…
On mixed finite element methods for first order elliptic systems
SummaryA physically based duality theory for first order elliptic systems is shown to be of central importance in connection with the Galerkin finite element solution of these systems. Using this…
Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, Wl, for 2 - p < oc. This implies that for functions in wf n W2 the error in…
Asymptotic expansions for finite element approximation of elliptic problem on polygonal domains
Experiences with Orthogonal Polynomials and „Best”︁ Numerical Integration Formulas on a Triangle; with Particular Reference to Finite Element Approximations
Fur einen Dreiecksbereich wird eine Folge homogener orthogonaler Polynome in naturlichen Dreieckskoordinaten konstruiert. Sie werden insbesondere auf gemeinsame Nullstellen und Punkte, in denen ihre…
Optimal stress locations in finite element models
The existence of optimal points for calculating accurate stresses within finite element models is discussed. A method for locating such points is proposed and applied to several popular finite…
Superconvcrgent estimation of the gradient from linear finite element approximations on triangular elements
  • Numerical Analysis Report 3 / 85 . Ph . D . Thesis
  • 1985
Superconvcrgent estimation of the gradient from linear finite element approximations on triangular elements. Numerical Analysis Report 3/85
  • Ph.D. Thesis,
  • 1985
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