On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type

Ivan Hlaváček; Michal Křížek

Aplikace matematiky (1987)

  • Volume: 32, Issue: 3, page 200-213
  • ISSN: 0862-7940

Abstract

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A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local O ( h 3 / 2 ) -superconvergence of the derivatives in the L 2 -norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.

How to cite

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Hlaváček, Ivan, and Křížek, Michal. "On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type." Aplikace matematiky 32.3 (1987): 200-213. <http://eudml.org/doc/15493>.

@article{Hlaváček1987,
abstract = {A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local $O(h^\{3/2\})$-superconvergence of the derivatives in the $L^2$-norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Aplikace matematiky},
keywords = {finite element; triangular elements; superconvergence; post-processing; averaged gradient; elliptic systems; finite element; triangular elements; superconvergence},
language = {eng},
number = {3},
pages = {200-213},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type},
url = {http://eudml.org/doc/15493},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Křížek, Michal
TI - On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 3
SP - 200
EP - 213
AB - A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local $O(h^{3/2})$-superconvergence of the derivatives in the $L^2$-norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.
LA - eng
KW - finite element; triangular elements; superconvergence; post-processing; averaged gradient; elliptic systems; finite element; triangular elements; superconvergence
UR - http://eudml.org/doc/15493
ER -

References

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  1. P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, New York, Oxford, 1978. (1978) Zbl0383.65058MR0520174
  2. 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
  3. I. Hlaváček J. Nečas, 10.1007/BF00249518, Arch. Rational Mech. Anal. 36 (1970), 305-311, 312-334. (1970) DOI10.1007/BF00249518
  4. M. Křížek P. Neittaanmäki, 10.1007/BF01379664, Numer. Math. 45 (1984), 105-116. (1984) MR0761883DOI10.1007/BF01379664
  5. L. A. Oganesjan L. A. Ruchovec, Variational-difference methods for the solution of elliptic equations, Izd. Akad. Nauk Armjanskoi SSR, Jerevan, 1979. (1979) 
  6. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  7. M. Zlámal, Some superconvergence results in the finite element method, Mathematical Aspects of Finite Element Methods (Proc. Conf., Rome, 1975). Springer-Verlag, Berlin, Heidelberg, New York, 1977, 353-362. (1975) MR0488863

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