Error estimates for external approximation of ordinary differential equations and the superconvergence property

Teresa Regińska

Displaying similar documents to “Error estimates for external approximation of ordinary differential equations and the superconvergence property”

Superconvergence of external approximation for two-point boundary problems

Teresa Regińska (1987)

Aplikace matematiky

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The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.

Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary

Van Bon Tran (1988)

Aplikace matematiky

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The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O (h)$ -convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O (h^{3 / 2})$ -convergence proved for a regular solution. Some a posteriori error estimates are also presented.

Shape optimization by means of the penalty method with extrapolation

Ivan Hlaváček (1994)

Applications of Mathematics

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A model shape optimal design in $ℝ^{2}$ is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.