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Displaying similar documents to “Convergence of dual finite element approximations for unilateral boundary value problems”

Internal finite element approximation in the dual variational method for the biharmonic problem

Ivan Hlaváček, Michal Křížek (1985)

Aplikace matematiky

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A conformal finite element method is investigated for a dual variational formulation of the biharmonic problem with mixed boundary conditions on domains with piecewise smooth curved boundary. Thus in the problem of elastic plate the bending moments are calculated directly. For the construction of finite elements a vector potential is used together with C 0 -elements. The convergence of the method is proved and an algorithm described.

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

Ivan Hlaváček, Michal Křížek (1984)

Aplikace matematiky

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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...