N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles

SUMMARYIn References 1 and 2 we showed that the error in the finite-element solution has two parts, the local error and the pollution error, and we studied the effect of the pollution error on the quality of the local error-indicators and the quality of the derivatives recovered by local post-processing. Here we show that it is possible to construct a posteriori estimates of the pollution error in any patch of elements by employing the local error-indicators over the mesh outside the patch. We also give an algorithm for the adaptive control of the pollution error in any patch of elements of interest.KEY WORDS finite-element method; a posteriori error estimation; pollution error

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A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method

Babuška

Strouboulis

Upadhyay

et al. 1995

Numerical Meth Engineering

103

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η%-Superconvergence of finite element approximations in the interior of general meshes of triangles

Babuška

Strouboulis

Upadhyay

1995

Computer Methods in Applied Mechanics and Engineering

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Superconvergence results on mildly structured triangulations

Lakhany

Marek

Whiteman

2000

Computer Methods in Applied Mechanics and Engineering

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N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles

Cited by 3 publications

References 1 publication

A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method

A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method

η%-Superconvergence of finite element approximations in the interior of general meshes of triangles

Superconvergence results on mildly structured triangulations

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