Eta%-Superconvergence in the Interior of Locally Refined Meshes of Quadrilaterals: Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations

Babuska, I.; Strouboulis, T.; Gangaraj, S. K.; Upadhyay, C. S.

doi:10.21236/ada277242

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…Obviously, a-posteriori error estimation for the high-order FEM is a challenging issue except in one-dimensional case. Many useful and effective methods and the techniques developed for the h-version of FEM can not be or have not been applied to the high-order FEM, such as the super-convergence and patch recovery techniques [13,[32][33][34][35]. The comprehensive analysis for a-posteriori error estimators and indicators based on the residuals for the p-and h-p of FEM in one dimension was well known in the mid of the 1980s [19,29], but these results can not be established in high dimensions, and techniques used for one-dimensional analysis can not be applied to two-and three-dimensional cases.…”

Section: Introductionmentioning

confidence: 99%

Recent progress on a-posteriori error analysis for the 𝑝 and ℎ-𝑝 finite element methods

Guo¹

2005

Recent Advances in Adaptive Computation

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This paper investigates recent progress on a-posteriori error analysis for the high-order finite element method(FEM). The paper will discuss the differences between a-posteriori error estimations for lower-order FEM and those for high-order FEM, and analyzes the technical and methodological differences on a-posteriori error estimations for high-order FEM in one dimension and in high dimensions. Based on a newly established mathematical framework of the Jacobi-weighted spaces, a-posterior error estimators and indicators for the p-and h-p version of FEM are proposed, and its prospective is discussed.

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Section: Introductionmentioning

confidence: 99%

Recent progress on a-posteriori error analysis for the 𝑝 and ℎ-𝑝 finite element methods

Guo¹

2005

Recent Advances in Adaptive Computation

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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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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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Adaptive numerical solution of thick plates using first‐order shear deformation theory. Part II: Adaptivity

Ludwig¹,

Shaw²,

Whiteman³

2003

Numerical Methods Partial

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This is the second in a pair of articles concerned with the adaptive finite element solution of RiessnerMindlin thick plates modeled using first-order shear deformation theory. This article is concerned with enhancing the a posteriori energy-error estimators developed in Part I in order to accomodate transition elements in the finite element mesh. The resulting estimators are then used in an adaptive finite element model employing transition elements and the subsequent results discussed and compared with those in Part I. A major part of the article is devoted to identifying a novel patch assembly node algorithm for using the ZZ recovery-type estimator with transition elements.

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Eta%-Superconvergence in the Interior of Locally Refined Meshes of Quadrilaterals: Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations

Cited by 3 publications

References 3 publications

Recent progress on a-posteriori error analysis for the 𝑝 and ℎ-𝑝 finite element methods

Recent progress on a-posteriori error analysis for the 𝑝 and ℎ-𝑝 finite element methods

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

Adaptive numerical solution of thick plates using first‐order shear deformation theory. Part II: Adaptivity

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