Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions

Ivan Hlaváček

Aplikace matematiky (1990)

  • Volume: 35, Issue: 5, page 405-417
  • ISSN: 0862-7940

Abstract

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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].

How to cite

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Hlaváček, Ivan. "Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions." Aplikace matematiky 35.5 (1990): 405-417. <http://eudml.org/doc/15639>.

@article{Hlaváček1990,
abstract = {A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {finite elements; penalty method; axisymmetric problems; extrapolation; a priori error estimates; finite element; a priori error estimates; penalty method; axisymmetric problems; extrapolation},
language = {eng},
number = {5},
pages = {405-417},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions},
url = {http://eudml.org/doc/15639},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 5
SP - 405
EP - 417
AB - A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].
LA - eng
KW - finite elements; penalty method; axisymmetric problems; extrapolation; a priori error estimates; finite element; a priori error estimates; penalty method; axisymmetric problems; extrapolation
UR - http://eudml.org/doc/15639
ER -

References

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  1. I. Babuška, The finite element method with penalty, Math. Соmр. 27, (1973), 221 - 228. (1973) MR0351118
  2. J. H. Bramble V. Thomée, Semidiscrete-least squares methods for a parabolic boundary value problem, Math. Соmр. 26 (1972), 633-648. (1972) MR0349038
  3. E.J.Haug K. Choi V. Komkov, Design sensitivity analysis of structural systems, Academic Press, London 1986. (1986) MR0860040
  4. I. Hlaváček M. Křížek, Dual finite element analysis of 3D-axisymmetric elliptic problems, (To appear). 
  5. I. Hlaváček, Domain optimization in axisymmetric elliptic boundary value problems by finite elements, Apl. Mat. 33 (1988), 213-244. (1988) MR0944785
  6. J. T. King, 10.1007/BF01459948, Numer. Math. 23, (1974), 153-165. (1974) Zbl0272.65092MR0400742DOI10.1007/BF01459948
  7. J. T. King S. M. Serbin, 10.1007/BF02252082, Computing 16 (1976), 339-347. (1976) MR0418485DOI10.1007/BF02252082
  8. J. Nečas, Les methodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  9. B. Mercier G. Raugel, 10.1051/m2an/1982160404051, RAIRO, Anal. numér. 16 (1982), 405-461. (1982) MR0684832DOI10.1051/m2an/1982160404051
  10. M. Zlámal, 10.1137/0710022, SfAM Numer. Anal. 10, (1973), 229-240. (1973) MR0395263DOI10.1137/0710022

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