Displaying similar documents to “Nonhomogeneous boundary conditions and curved triangular finite elements”

Curved triangular finite C m -elements

Alexander Ženíšek (1978)

Aplikace matematiky

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Curved triangular C m -elements which can be pieced together with the generalized Bell’s C m -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order 2 ( m + 1 ) in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same...

Numerical analysis of the general biharmonic problem by the finite element method

Jiří Hřebíček (1982)

Aplikace matematiky

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The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit C 1 -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform V O h -ellipticity are found.

On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type

Ivan Hlaváček, Michal Křížek (1987)

Aplikace matematiky

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A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton’s or Neumann’s type. For bounded plane domains with smooth boundary the local O ( h 3 / 2 ) -superconvergence of the derivatives in the L 2 -norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet’s boundary conditions is treated.