Superconvergence of the gradient of finite element solutions

Lesaint, P.; Zlámal, Miloš

doi:10.1051/m2an/1979130201391

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Introduction3

Direct Superconvergence1

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1987

2009

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Cited by 69 publications

(47 citation statements)

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“…The values of the solution quantities are obtained by direct evaluation from the finite element solution at special points, the superconvergence points for the solution quantity in the element (see, among others, (6], [10], [13], [14], [47] and [50]).…”

Section: Direct Superconvergencementioning

confidence: 99%

Validation of Recipes for the Recovery of Stresses and Derivatives by a Computer-Based Approach

Babuska¹,

Strouboulis²,

Gangaraj³

et al. 1994

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Section: Direct Superconvergencementioning

confidence: 99%

Validation of Recipes for the Recovery of Stresses and Derivatives by a Computer-Based Approach

Babuska¹,

Strouboulis²,

Gangaraj³

et al. 1994

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“…By Lemma 1.1, the estimate (1. [4,10,16,18,24,25]. This implies that the Lagrange interpolation associated with the Lobatto points and the finite element solution are superclose by one order in H 1 norm.…”

Section: Introductionmentioning

confidence: 98%

Lagrange interpolation and finite element superconvergence

2003

Numerical Methods Partial

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Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Q k -type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the finite element solution are superclose in H 1 norm. For d-dimensional P k -type elements, we consider the standard Lagrange interpolation-the Lagrange interpolation with interpolation points being the principle lattice points of simplicial elements. We prove for d ≥ 2 and k ≥ d + 1 that such interpolation and the finite element solution are not superclose in both H 1 and L 2 norms, and that not all such interpolation points are superconvergence points for the finite element approximation.

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