On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions

Brandts, Jan; Korotov, Sergey; Kříek, Michal

doi:10.1016/j.camwa.2007.11.010

Cited by 55 publications

(50 citation statements)

References 14 publications

(12 reference statements)

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“…, 2 and notice at the end that after finitely many steps the areas of one-dimensional facets are just t j = 1. Lemma 3 thus follows from (6) and (8) by induction.…”

Section: Lemma 3 Let F Be a Semiregular Family Of Partitions Of A Pomentioning

confidence: 88%

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On Synge-type angle condition for $d$-simplices

Hannukainen

Korotov

Křížek³

2017

Appl.Math.

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Abstract. The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in R d that degenerate in some way.

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“…, 2 and notice at the end that after finitely many steps the areas of one-dimensional facets are just t j = 1. Lemma 3 thus follows from (6) and (8) by induction.…”

Section: Lemma 3 Let F Be a Semiregular Family Of Partitions Of A Pomentioning

confidence: 88%

“…Further (equivalent) definitions of the regularity of a family of partitions of a polytope into simplices are presented in [6], [7].…”

mentioning

confidence: 99%

On Synge-type angle condition for $d$-simplices

Hannukainen

Korotov

Křížek³

2017

Appl.Math.

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“…Several variants of the algorithm suitable for standard FEMs were also proposed, analysed and numerically tested in [1,2,3,8,10,11] (see also references therein). It has been commonly noticed that inspite of a general simplicity of this type of bisection algorithms, it turns to be hard to provide mesh conformity and simultaneously to prove relevant mesh regularity results [4,20], especially in the case of local mesh refinements and in higher dimensions.…”

Section: Introductionmentioning

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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“…In addition, in [2] the following minimum angle condition was presented and its equivalence with the above three, (1)…”

Section: On Mesh Regularity Conditionsmentioning

confidence: 99%