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Approximations by the Cauchy-type integrals with piecewise linear densities

Jaroslav Drobek (2012)

Applications of Mathematics

The paper is a contribution to the complex variable boundary element method, shortly CVBEM. It is focused on Jordan regions having piecewise regular boundaries without cusps. Dini continuous densities whose modulus of continuity ω ( · ) satisfies lim sup s 0 ω ( s ) ln 1 s = 0 are considered on these boundaries. Functions satisfying the Hölder condition of order α , 0 < α 1 , belong to them. The statement that any Cauchy-type integral with such a density can be uniformly approximated by a Cauchy-type integral whose density is a piecewise...

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

Ivan Hlaváček, Michal Křížek (1985)

Aplikace matematiky

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.

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