On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition

Ivan Hlaváček; Michal Křížek

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

Ivan Hlaváček, Michal Křížek (1987)

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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.

The finite element solution of second order elliptic problems with the Newton boundary condition

Libor Čermák (1983)

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The convergence of the finite element solution for the second order elliptic problem in the $n$ -dimensional bounded domain $(n \geq 2)$ with the Newton boundary condition is analysed. The simplicial isoparametric elements are used. The error estimates in both the $H^{1}$ and $L_{2}$ norms are obtained.

Finite elements methods for solving viscoelastic thin plates

Helena Růžičková, Alexander Ženíšek (1984)

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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.

Convergence of a finite element method based on the dual variational formulation

Jaroslav Haslinger, Ivan Hlaváček (1976)

Aplikace matematiky

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