Displaying similar documents to “The finite element solution of second order elliptic problems with the Newton boundary condition”

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.

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.