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

Ivan Hlaváček; Michal Křížek

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.

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

Libor Čermák (1983)

Aplikace matematiky

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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.

Displaying similar documents to “On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition”

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

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