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

Aplikace matematiky (1980)

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

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topHlaváček, 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

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

## Citations in EuDML Documents

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

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