Strongly regular family of boundary-fitted tetrahedral meshes of bounded C 2 domains

Radim Hošek

Applications of Mathematics (2016)

  • Volume: 61, Issue: 3, page 233-251
  • ISSN: 0862-7940

Abstract

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We give a constructive proof that for any bounded domain of the class C 2 there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by Křížek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below and shown to converge to a positive number by virtue of the convergence of q -Pochhammer symbol. The final result takes the form of an implication with an assumption that can be obviously fulfilled for any bounded C 2 domain.

How to cite

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Hošek, Radim. "Strongly regular family of boundary-fitted tetrahedral meshes of bounded $C^2$ domains." Applications of Mathematics 61.3 (2016): 233-251. <http://eudml.org/doc/276993>.

@article{Hošek2016,
abstract = {We give a constructive proof that for any bounded domain of the class $C^2$ there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by Křížek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below and shown to converge to a positive number by virtue of the convergence of $q$-Pochhammer symbol. The final result takes the form of an implication with an assumption that can be obviously fulfilled for any bounded $C^2$ domain.},
author = {Hošek, Radim},
journal = {Applications of Mathematics},
keywords = {boundary fitted mesh; strongly regular family; Sommerville tetrahedron; Sommerville regularity ratio; mesh refinement; tetrahedral mesh; boundary fitted mesh; strongly regular family; Sommerville tetrahedron; Sommerville regularity ratio; mesh refinement; tetrahedral mesh},
language = {eng},
number = {3},
pages = {233-251},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Strongly regular family of boundary-fitted tetrahedral meshes of bounded $C^2$ domains},
url = {http://eudml.org/doc/276993},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Hošek, Radim
TI - Strongly regular family of boundary-fitted tetrahedral meshes of bounded $C^2$ domains
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 233
EP - 251
AB - We give a constructive proof that for any bounded domain of the class $C^2$ there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by Křížek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated from below and shown to converge to a positive number by virtue of the convergence of $q$-Pochhammer symbol. The final result takes the form of an implication with an assumption that can be obviously fulfilled for any bounded $C^2$ domain.
LA - eng
KW - boundary fitted mesh; strongly regular family; Sommerville tetrahedron; Sommerville regularity ratio; mesh refinement; tetrahedral mesh; boundary fitted mesh; strongly regular family; Sommerville tetrahedron; Sommerville regularity ratio; mesh refinement; tetrahedral mesh
UR - http://eudml.org/doc/276993
ER -

References

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  1. Audin, M., 10.1007/978-3-642-56127-6, Universitext Springer, Berlin (2003), 2012. Zbl1194.01029MR1941838DOI10.1007/978-3-642-56127-6
  2. Brandts, J., Korotov, S., Křížek, M., 10.1016/j.aml.2009.01.031, Appl. Math. Lett. 22 1210-1212 (2009). (2009) MR2532540DOI10.1016/j.aml.2009.01.031
  3. Edelsbrunner, H., 10.1017/S0962492900001331, Acta Numerica 9 133-213 (2000). (2000) Zbl1004.65024MR1883628DOI10.1017/S0962492900001331
  4. Evans, L. C., Partial Differential Equations, Graduate Studies in Mathematics 19 American Mathematical Society, Providence (1998). (1998) Zbl0902.35002MR1625845
  5. Feireisl, E., Hošek, R., Maltese, D., Novotný, A., 10.1051/m2an/2016022, (to appear) in ESAIM, Math. Model. Numer. Anal. (2016). Preprint IM-2015-46, available at http://math.cas.cz/fichier/preprints/IM_20150826112605_92.pdf, 2015. DOI10.1051/m2an/2016022
  6. Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press Cambridge (2013). (2013) Zbl1267.15001MR2978290
  7. Hošek, R., 10.1007/s10492-015-0115-5, Appl. Math., Praha 60 637-651 (2015). (2015) Zbl1363.65209MR3436566DOI10.1007/s10492-015-0115-5
  8. Korotov, S., Křížek, M., Neittaanmäki, P., 10.1023/A:1022268103114, Appl. Math., Praha 44 33-42 (1999). (1999) Zbl1060.65665MR1666850DOI10.1023/A:1022268103114
  9. Křížek, M., An equilibrium finite element method in three-dimensional elasticity, Apl. Mat. 27 46-75 (1982). (1982) Zbl0488.73072MR0640139
  10. Sommerville, D. M. Y., Space-filling tetrahedra in Euclidean space, Proc. Edinburgh Math. Soc. 41 49-57 (1923). (1923) 
  11. Zhang, S., Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes, Houston J. Math. 21 541-556 (1995). (1995) Zbl0855.65124MR1352605

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