On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates

Ivan Hlaváček; Michal Křížek

Aplikace matematiky (1987)

  • Volume: 32, Issue: 4, page 276-289
  • ISSN: 0862-7940

Abstract

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Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order O ( h 2 ) are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.

How to cite

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Hlaváček, Ivan, and Křížek, Michal. "On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates." Aplikace matematiky 32.4 (1987): 276-289. <http://eudml.org/doc/15500>.

@article{Hlaváček1987,
abstract = {Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order $O(h^2)$ are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Aplikace matematiky},
keywords = {post-processing; averaged gradient; elliptic systems; second order elliptic systems; linear finite elements; regular uniform triangulations; error estimats; optimal order; superconvergence; post-processing; averaged gradient; elliptic systems; Second order elliptic systems; linear finite elements; regular uniform triangulations; Error estimats; optimal order},
language = {eng},
number = {4},
pages = {276-289},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates},
url = {http://eudml.org/doc/15500},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Křížek, Michal
TI - On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 4
SP - 276
EP - 289
AB - Second order elliptic systems with boundary conditions of Dirichlet, Neumann’s or Newton’s type are solved by means of linear finite elements on regular uniform triangulations. Error estimates of the optimal order $O(h^2)$ are proved for the averaged gradient on any fixed interior subdomain, provided the problem under consideration is regular in a certain sense.
LA - eng
KW - post-processing; averaged gradient; elliptic systems; second order elliptic systems; linear finite elements; regular uniform triangulations; error estimats; optimal order; superconvergence; post-processing; averaged gradient; elliptic systems; Second order elliptic systems; linear finite elements; regular uniform triangulations; Error estimats; optimal order
UR - http://eudml.org/doc/15500
ER -

References

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  8. I. Hlaváček M. Křížek, On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary conditions, Apl. Mat. 32 (1987), 131-154. (1987) MR0885758
  9. I. Hlaváček M. Křížek, On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type, Apl. Mat. 32 (1987), 200-213. (1987) MR0895878
  10. J. Kadlec, On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set, Czechoslovak Math. J. 14 (1964), 386-393. (1964) Zbl0166.37703MR0170088
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  12. M. Moussaoui, Régularité de la solution d'un problème à derivée oblique, Comptes Rendus Acad. Sci. Paris, 279, sér. A, 25 (1974), 869-872. (1974) Zbl0293.35014MR0358062
  13. J. Nečas, Les méthodes directes en theorie des équations elliptiques, Masson, Paris, or Academia, Prague, 1967. (1967) MR0227584
  14. J. A. Nitsche A. H. Schatz, Interior estimate for Ritz-Galerkin methods, Math. Соmр. 28 (1974), 937-958. (1974) MR0373325
  15. B. Westergren, Interior estimates for elliptic systems of difference equations, (Thesis), Univ. of Göteborg, 1982. (1982) 
  16. Q. D. Zhu, Natural inner superconvergence for the finite element method, Proc. China-France Sympos. on Finite Element Methods, Beijing, 1982, Gordon and Breach, Sci. Publ., Inc., New York, 1983, 935-960. (1982) MR0754041

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