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

Aplikace matematiky (1987)

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

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topHlaváček, 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

top- P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, New York, Oxford, 1978. (1978) Zbl0383.65058MR0520174
- I. Hlaváček M. Křížek, On a superconvergent finite element scheme for elliptic systems, I. Dirichlet boundary conditions, Apl. Mat. 32 (1987), 131 -154. (1987) Zbl0622.65097MR0885758
- I. Hlaváček J. Nečas, 10.1007/BF00249518, Arch. Rational Mech. Anal. 36 (1970), 305-311, 312-334. (1970) Zbl0193.39002DOI10.1007/BF00249518
- M. Křížek P. Neittaanmäki, 10.1007/BF01379664, Numer. Math. 45 (1984), 105-116. (1984) Zbl0575.65104MR0761883DOI10.1007/BF01379664
- L. A. Oganesjan L. A. Ruchovec, Variational-difference methods for the solution of elliptic equations, Izd. Akad. Nauk Armjanskoi SSR, Jerevan, 1979. (1979)
- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
- 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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