| Title:
|
Strongly regular family of boundary-fitted tetrahedral meshes of bounded $C^2$ domains (English) |
| Author:
|
Hošek, Radim |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
233-251 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
boundary fitted mesh |
| Keyword:
|
strongly regular family |
| Keyword:
|
Sommerville tetrahedron |
| Keyword:
|
Sommerville regularity ratio |
| Keyword:
|
mesh refinement |
| Keyword:
|
tetrahedral mesh |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 06587851 |
| idMR:
|
MR3502110 |
| DOI:
|
10.1007/s10492-016-0130-1 |
| . |
| Date available:
|
2016-05-19T08:49:11Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145699 |
| . |
| Reference:
|
[1] Audin, M.: Geometry.Universitext Springer, Berlin (2003), 2012. Zbl 1194.01029, MR 1941838, 10.1007/978-3-642-56127-6 |
| Reference:
|
[2] Brandts, J., Korotov, S., Křížek, M.: On the equivalence of ball conditions for simplicial finite elements in ${\mathbb R}^d$.Appl. Math. Lett. 22 1210-1212 (2009). MR 2532540, 10.1016/j.aml.2009.01.031 |
| Reference:
|
[3] Edelsbrunner, H.: Triangulations and meshes in computational geometry.Acta Numerica 9 133-213 (2000). Zbl 1004.65024, MR 1883628, 10.1017/S0962492900001331 |
| Reference:
|
[4] Evans, L. C.: Partial Differential Equations.Graduate Studies in Mathematics 19 American Mathematical Society, Providence (1998). Zbl 0902.35002, MR 1625845 |
| Reference:
|
[5] Feireisl, E., Hošek, R., Maltese, D., Novotný, A.: Error estimates for a numerical method for the compressible Navier-{S}tokes system on sufficiently smooth domains.(to appear) in ESAIM, Math. Model. Numer. Anal. (2016). Preprint IM-2015-46, available at http://math.cas.cz/fichier/preprints/IM\char'137 20150826112605\char'137 92.pdf, 2015. 10.1051/m2an/2016022 |
| Reference:
|
[6] Horn, R. A., Johnson, C. R.: Matrix Analysis.Cambridge University Press Cambridge (2013). Zbl 1267.15001, MR 2978290 |
| Reference:
|
[7] Hošek, R.: Face-to-face partition of 3{D} space with identical well-centered tetrahedra.Appl. Math., Praha 60 637-651 (2015). Zbl 1363.65209, MR 3436566, 10.1007/s10492-015-0115-5 |
| Reference:
|
[8] Korotov, S., Křížek, M., Neittaanmäki, P.: On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary.Appl. Math., Praha 44 33-42 (1999). Zbl 1060.65665, MR 1666850, 10.1023/A:1022268103114 |
| Reference:
|
[9] Křížek, M.: An equilibrium finite element method in three-dimensional elasticity.Apl. Mat. 27 46-75 (1982). Zbl 0488.73072, MR 0640139 |
| Reference:
|
[10] Sommerville, D. M. Y.: Space-filling tetrahedra in Euclidean space.Proc. Edinburgh Math. Soc. 41 49-57 (1923). |
| Reference:
|
[11] Zhang, S.: Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes.Houston J. Math. 21 541-556 (1995). Zbl 0855.65124, MR 1352605 |
| . |
