Displaying similar documents to “Numerical analysis of the general biharmonic problem by the finite element method”

Nonhomogeneous boundary conditions and curved triangular finite elements

Alexander Ženíšek (1981)

Aplikace matematiky

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Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order 2 m + 2 , in the second part of the paper in the case of nonhomogeneous mixed boundary value problem...

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.

Finite elements methods for solving viscoelastic thin plates

Helena Růžičková, Alexander Ženíšek (1984)

Aplikace matematiky

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The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by C 1 -elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.

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...