Displaying similar documents to “Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries”

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.

Dual finite element analysis of axisymmetric elliptic problems with an absolute term

Ivan Hlaváček (1991)

Applications of Mathematics

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A model second order elliptic equation in cylindrical coordinates with mixed boundary conditions is considered. A dual variational formulation is employed to calculate the cogradient of the solution directly. Approximations are defined on the basis of standard finite elements spaces. Convergence analysis and some a posteriori error estimates are presented.

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

Aplikace matematiky

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The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. ...