Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries

Ivan Hlaváček; Michal Křížek

Aplikace matematiky (1984)

  • Volume: 29, Issue: 1, page 52-69
  • ISSN: 0862-7940

Abstract

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Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.

How to cite

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Hlaváček, Ivan, and Křížek, Michal. "Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries." Aplikace matematiky 29.1 (1984): 52-69. <http://eudml.org/doc/15333>.

@article{Hlaváček1984,
abstract = {Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Aplikace matematiky},
keywords = {dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence; dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence},
language = {eng},
number = {1},
pages = {52-69},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries},
url = {http://eudml.org/doc/15333},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Křížek, Michal
TI - Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 1
SP - 52
EP - 69
AB - Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.
LA - eng
KW - dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence; dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence
UR - http://eudml.org/doc/15333
ER -

References

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  14. J. Penman J. R. Fraser, 10.1109/TMAG.1982.1061883, IEEE Trans. on Magnetics 18 (1982), 319-324. (1982) DOI10.1109/TMAG.1982.1061883
  15. G. Strang G. J. Fix, An analysis of the finite element method, Prentice Hall, New Jersey, 1973. (1973) MR0443377
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