Article
Full entry |
PDF
(2.4 MB)
Feedback
PDF
(2.4 MB)
Feedback
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
Summary:
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.
References:
[1] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation. Apl. mat. 21 (1976), 43 - 65. MR 0398126
[2] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements. Int. J. Numer. Meth. Eng. 5 (1972), 65 - 82. DOI 10.1002/nme.1620050107
[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
[4] O. A. Ladyzenskaya: The mathematical theory of viscous incompressible flow. Gordon & Breach, New York 1969. MR 0254401
Search
Partner of
