Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek; Pekka Neittaanmäki

Aplikace matematiky (1984)

  • Volume: 29, Issue: 4, page 272-285
  • ISSN: 0862-7940

Abstract

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The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.

How to cite

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Křížek, Michal, and Neittaanmäki, Pekka. "Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains." Aplikace matematiky 29.4 (1984): 272-285. <http://eudml.org/doc/15357>.

@article{Křížek1984,
abstract = {The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.},
author = {Křížek, Michal, Neittaanmäki, Pekka},
journal = {Aplikace matematiky},
keywords = {Maxwell equations; finite element method; div-rot system; mixed boundary conditions; piecewise smooth boundary; Piecewise linear element fields; numerical examples; Maxwell equations; finite element method; div-rot system; mixed boundary conditions; piecewise smooth boundary; Piecewise linear element fields; Numerical examples},
language = {eng},
number = {4},
pages = {272-285},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains},
url = {http://eudml.org/doc/15357},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Křížek, Michal
AU - Neittaanmäki, Pekka
TI - Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 4
SP - 272
EP - 285
AB - The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given.
LA - eng
KW - Maxwell equations; finite element method; div-rot system; mixed boundary conditions; piecewise smooth boundary; Piecewise linear element fields; numerical examples; Maxwell equations; finite element method; div-rot system; mixed boundary conditions; piecewise smooth boundary; Piecewise linear element fields; Numerical examples
UR - http://eudml.org/doc/15357
ER -

References

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  1. J. H. Bramble A. H. Schatz, Least squares methods for 2m th order elliptic boundary-value problems, Math. Сотр. 25 (1971), 1-32. (1971) MR0295591
  2. P. G. Ciarlet, The finite element method for elliptic problems, North-Hiolland Publishing Company, Amsterdam, New York, Oxford, 1978. (1978) Zbl0383.65058MR0520174
  3. M. Crouzeix A. Y. Le Roux, Ecoulement d'une fluide irrotationnel. Journées Elements Finis, Université de Rennes, Rennes, 1976. (1976) 
  4. P. Doktor, On the density of smooth functions in certain subspaces of Sobolev spaces, Comment. Math. Univ. Carolin. 14, 4 (1973), 609-622. (1973) MR0336317
  5. G. J. Fix M. D. Gunzburher R. A. Nicolaides, 10.1007/BF01396185, Numer. Math. 37 (1981), 29-48. (1981) MR0615890DOI10.1007/BF01396185
  6. V. Girault P. A. Raviart, Finite element approximation of the Navier-Stokes equation, Springer-Verlag, Berlin, Heidelberg, New York, 1979. (1979) MR0548867
  7. P. Grisvard, Behaviour of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, Numerical Solution of Partial Differential Equations III, Academic Press, New York, 1976, 207-274. (1976) MR0466912
  8. J. Haslinger P. Neittaanmäki, 10.1016/0045-7825(84)90022-7, Comput. Methods Appl. Mech. Engrg. 42 (1984), 131-148. (1984) MR0737949DOI10.1016/0045-7825(84)90022-7
  9. M. Křížek, 10.1051/m2an/1983170100351, RAIRO Anal. Numer. 17 (1983), 35-65. (1983) MR0695451DOI10.1051/m2an/1983170100351
  10. M. Křížek P. Neittaanmäki, On the validity of Friedrich's inequalities, Math. Scand. (to appear). MR0753060
  11. R. Leis, Anfangsrandwertaufgaben der mathematischen Physik, SFB 74, Bonn, preprint. Zbl0474.35002MR1290369
  12. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  13. J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies: an introduction, Elsevier Scientific Publishing Company, Amsterdam, Oxford. New York, 1981. (1981) MR0600655
  14. P. Neittaanmäki R. Picard, 10.1016/0898-1221(81)90111-5, J. Comput. Math. Appl. 7 (1981), 127-138. (1981) MR0619754DOI10.1016/0898-1221(81)90111-5
  15. P. Neittaanmäki J. Saranen, 10.1002/mma.1670030124, Math. Meth. Appl. Sci. 3 (1981), 328-335. (1981) MR0657301DOI10.1002/mma.1670030124
  16. P. Neittaanmäki J. Saranen, 10.1016/0771-050X(82)90038-9, J. Comput. Appl. Math. 8 (1982), 165-169. (1982) DOI10.1016/0771-050X(82)90038-9
  17. J. Saranen, Über die Approximation der Lösungen der Maxwellschen Randwertaufgabe mil der Methode der finiten Elemente, Applicable Anal. 10 (1980), 15 - 30. (1980) MR0572804
  18. J. Saranen, 10.1080/00036818208839407, Applicable Anal. 14 (1982), 27-42. (1982) Zbl0478.65065MR0678492DOI10.1080/00036818208839407
  19. I. N. Sneddon, Mixed boundary value problems in potential theory, North-Holland Publishing Company, Amsterdam, 1966. (1966) Zbl0139.28801MR0216018
  20. J. M. Thomas, Sur l'analyse numérique des méthodes d'éléments finis hybrides et mixtes, Thesis, Université Paris VI, 1977. (1977) 
  21. W. L. Wendland E. Stephan G. C. Hsiao, 10.1002/mma.1670010302, Math. Meth. Appl. Sci. 1 (1979), 265-321. (1979) MR0548943DOI10.1002/mma.1670010302

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