| Title:
|
On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary (English) |
| Author:
|
Korotov, Sergey |
| Author:
|
Křížek, Michal |
| Author:
|
Neittaanmäki, Pekka |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
33-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we present an algorithm for a construction of strongly regular families of triangulations for planar domains with a piecewise curved boundary. Some additional properties of the resulting triangulations are considered. (English) |
| Keyword:
|
strongly regular family |
| Keyword:
|
triangulation |
| Keyword:
|
planar domain |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1060.65665 |
| idMR:
|
MR1666850 |
| DOI:
|
10.1023/A:1022268103114 |
| . |
| Date available:
|
2009-09-22T17:59:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134404 |
| . |
| Reference:
|
[1] Bänsch, E.: Local mesh refinement in 2 and 3 dimensions.Impact Comput. Sci. Engrg. 3 (1991), 181–191. MR 1141298, 10.1016/0899-8248(91)90006-G |
| Reference:
|
[2] Ciarlet, P. G.: Basic error estimates for elliptic problems, Handbook of Numer. Anal. (ed. P. G. Ciarlet, J. L. Lions).North-Holland, Amsterdam, 1991, pp. 17–351. MR 1115237 |
| Reference:
|
[3] George, P. L.: Automatic mesh generation.John Wiley & Sons, New York, 1991. Zbl 0808.65122, MR 1165297 |
| Reference:
|
[4] Joe, B.: Delaunay triangular meshes in convex polygons.SIAM J. Sci. Stat. Comput. 7 (1986), 514–539. Zbl 0637.65121, MR 0833919, 10.1137/0907035 |
| Reference:
|
[5] Korneev, V. G.: Schemes of the finite element method for high orders of accuracy.Leningrad University, Leningrad, 1977, (in Russian). Zbl 0481.65062, MR 0518815 |
| Reference:
|
[6] Koukal, S., Křížek, M.: Curved affine quadratic finite elements.J. Comput. Appl. Math. 63 (1995), 333–339. MR 1365573, 10.1016/0377-0427(95)00061-5 |
| Reference:
|
[7] Křížek, M., Neittaanmäki, P.: Mathematical and numerical modelling in electrical engineering. Theory and applications.Kluwer, Dordrecht, 1996. MR 1431889 |
| Reference:
|
[8] Lin, Q., Xu, J. Ch.: Linear finite elements with high accuracy.J. Comput. Math. 3 (1985), 115–133. MR 0854355 |
| Reference:
|
[9] Matsokin, A. M.: Automatic triangulation of domains with smooth boundaries for solving equations of the elliptic type.Preprint of Computer Center, 15, Novosibirsk, 1975, (in Russian). |
| Reference:
|
[10] Mosco, U.: Convergence of convex sets and of solutions of variational inequalities.Adv. in Math. 3 (1969), 510–585. Zbl 0192.49101, MR 0298508, 10.1016/0001-8708(69)90009-7 |
| Reference:
|
[11] Rosenberg, I. G., Stenger, F.: A lower bound on the angle of triangles constructed by bisecting the longest side.Math. Comp. 29 (1975), 390–395. MR 0375068, 10.1090/S0025-5718-1975-0375068-5 |
| Reference:
|
[12] Zlámal, M.: Curved elements in the finite element method.SIAM J. Numer. Anal. 10 (1973), 229–240. MR 0395263, 10.1137/0710022 |
| . |
