Displaying similar documents to “On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type”

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

Ivan Hlaváček, Michal Křížek (1987)

Aplikace matematiky

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Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate O ( h 3 / 2 ) is proved in the L 2 -norm. For a class of polygonal domains the global estimate O ( h 2 ) can be proven.

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.