On superconvergence techniques

Křížek, Michal; Neittaanmäki, Pekka

doi:10.1007/bf00047538

Cited by 157 publications

(31 citation statements)

References 137 publications

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“…A suitable postprocessing operator based on the supercloseness phenomenon (3.1) can be developed to improve the approximation order of the gradients of finite element solutions from O(h) to O(h 2 ). From then on, the supercloseness property (3.1) between the finite element solution and the interpolant of the exact solution has played an important and essential role in getting many superconvergence results (see [3], [4], [7], [11], [13], [18], [21], and references therein). In one space dimension, the supercloseness of the finite element solution was considered by Tong in 1969 (see [20]).…”

Section: Superclosenessmentioning

confidence: 99%

What is the smallest possible constant in Céa’s lemma?

Chen

Křížek²

2006

Appl Math

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Section: Superclosenessmentioning

confidence: 99%

What is the smallest possible constant in Céa’s lemma?

Chen

Křížek²

2006

Appl Math

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“…For the literature, the reader is referred to [1,2,4,9,10,14,15,16,22,26,27] and references therein. Here, by "natural superconvergence," we mean that the superconvergence points are obtained without employing any postprocessing in FE solutions.…”

Section: Introductionmentioning

confidence: 99%

Natural Superconvergence Points in Three-Dimensional Finite Elements

Lin¹,

Zhang²

2008

SIAM J. Numer. Anal.

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Abstract.A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C 0 finite elements in a three-dimensional setting. This identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces. Derivative and function value superconvergence points are investigated for both the Poisson and the Laplace equations. Superconvergence results are reported for hexahedral, pentahedral, and tetrahedral elements up to certain degrees.

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“…Hereũ is a higher order approximation of the exact solution of some boundary value problem and u h is a numerical approximation of the true solution. The functionũ can be obtained, e.g., by some averaging superconvergence technique [9].…”

Section: Numerical Resultsmentioning

confidence: 99%

On a Bisection Algorithm That Produces Conforming Locally Refined Simplicial Meshes

Hannukainen¹,

Korotov

Křížek

2010

Large-Scale Scientific Computing

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Antti Hannukainen, Sergey Korotov, Michal Křížek: On a bisection algorithm that produces conforming locally refined simplicial meshes; Helsinki University of Technology Institute of Mathematics Research Reports A567 (2009).Abstract: First we introduce a mesh density function that serves as a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse. Further, we propose a new bisection algorithm that chooses for bisection an edge in a given mesh associated with the maximum value of the mesh density function. Dividing this edge at its midpoint, we correspondingly bisect all simplices sharing this edge. Repeating this process, we construct a family of conforming nested simplicial meshes. We prove that the corresponding mesh size tends to zero for d = 2, 3. AMS subject classifications: 65N50, 65M50Keywords: bisection algorithm, simplicial elements, conforming finite element method, local refinements, nested meshes

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On superconvergence techniques

Cited by 157 publications

References 137 publications

What is the smallest possible constant in Céa’s lemma?

What is the smallest possible constant in Céa’s lemma?

Natural Superconvergence Points in Three-Dimensional Finite Elements

On a Bisection Algorithm That Produces Conforming Locally Refined Simplicial Meshes

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