The density of solenoidal functions and the convergence of a dual finite element method

Ivan Hlaváček

Aplikace matematiky (1980)

  • Volume: 25, Issue: 1, page 39-55
  • ISSN: 0862-7940

Abstract

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A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.

How to cite

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Hlaváček, Ivan. "The density of solenoidal functions and the convergence of a dual finite element method." Aplikace matematiky 25.1 (1980): 39-55. <http://eudml.org/doc/15129>.

@article{Hlaváček1980,
abstract = {A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {density of solenoidal functions; convergence of a dual finite element method; Dirichlet; Neumann and a mixed boundary value problem; second order elliptic equation; density of solenoidal functions; convergence of a dual finite element method; Dirichlet, Neumann and a mixed boundary value problem; second order elliptic equation},
language = {eng},
number = {1},
pages = {39-55},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The density of solenoidal functions and the convergence of a dual finite element method},
url = {http://eudml.org/doc/15129},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - The density of solenoidal functions and the convergence of a dual finite element method
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 1
SP - 39
EP - 55
AB - A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.
LA - eng
KW - density of solenoidal functions; convergence of a dual finite element method; Dirichlet; Neumann and a mixed boundary value problem; second order elliptic equation; density of solenoidal functions; convergence of a dual finite element method; Dirichlet, Neumann and a mixed boundary value problem; second order elliptic equation
UR - http://eudml.org/doc/15129
ER -

References

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  1. J. Haslinger I. Hlaváček, Convergence of a finite element method based on the dual variational formulation, Apl. mat. 21 (1976), 43 - 65. (1976) MR0398126
  2. B. Fraeijs de Veubeke M. Hogge, 10.1002/nme.1620050107, Int. J. Numer. Meth. Eng. 5 (1972), 65 - 82. (1972) DOI10.1002/nme.1620050107
  3. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  4. O. A. Ladyzenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach, New York 1969. (1969) MR0254401

Citations in EuDML Documents

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  1. Ivan Hlaváček, Optimization of the domain in elliptic problems by the dual finite element method
  2. Juraj Weisz, A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem
  3. Ivan Hlaváček, Michal Křížek, Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
  4. Michal Křížek, Conforming equilibrium finite element methods for some elliptic plane problems

NotesEmbed ?

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