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

top
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

top

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

top
  1. I. Babuška, The finite element method with penalty, Math. Соmр. 27, (1973), 221 - 228. (1973) Zbl0299.65057MR0351118
  2. J. H. Bramble V. Thomée, Semidiscrete-least squares methods for a parabolic boundary value problem, Math. Соmр. 26 (1972), 633-648. (1972) Zbl0268.65060MR0349038
  3. E.J.Haug K. Choi V. Komkov, Design sensitivity analysis of structural systems, Academic Press, London 1986. (1986) Zbl0618.73106MR0860040
  4. I. Hlaváček M. Křížek, Dual finite element analysis of 3D-axisymmetric elliptic problems, (To appear). Zbl0786.65090
  5. I. Hlaváček, Domain optimization in axisymmetric elliptic boundary value problems by finite elements, Apl. Mat. 33 (1988), 213-244. (1988) Zbl0677.65102MR0944785
  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) Zbl0338.65054MR0418485DOI10.1007/BF02252082
  8. J. Nečas, Les methodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  9. B. Mercier G. Raugel, Resolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en θ , RAIRO, Anal. numér. 16 (1982), 405-461. (1982) Zbl0531.65054MR0684832
  10. M. Zlámal, 10.1137/0710022, SfAM Numer. Anal. 10, (1973), 229-240. (1973) MR0395263DOI10.1137/0710022

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.