×

zbMATH — the first resource for mathematics

On the existence of strongly regular families of triangulations for domains with a piecewise smooth boundary. (English) Zbl 1060.65665
The authors give a constructive proof of the existence of strongly regular families of triangulations for planar domains with piecewise curved boundaries. The algorithm for the construction is described. Some additional properties of the resulting triangulations are discussed.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Bänsch, E.: Local mesh refinement in 2 and 3 dimensions. Impact Comput. Sci. Engrg. 3 (1991), 181-191. · Zbl 0744.65074
[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. · Zbl 0875.65086
[3] George, P. L.: Automatic mesh generation. John Wiley & Sons, New York, 1991. · Zbl 0808.65122
[4] Joe, B.: Delaunay triangular meshes in convex polygons. SIAM J. Sci. Stat. Comput. 7 (1986), 514-539. · Zbl 0637.65121
[5] Korneev, V. G.: Schemes of the finite element method for high orders of accuracy. Leningrad University, Leningrad, 1977) · Zbl 0481.65062
[6] Koukal, S., Křížek, M.: Curved affine quadratic finite elements. J. Comput. Appl. Math. 63 (1995), 333-339. · Zbl 0853.65118
[7] Křížek, M., Neittaanmäki, P.: Mathematical and numerical modelling in electrical engineering. Theory and applications. Kluwer, Dordrecht, 1996.
[8] Lin, Q., Xu, J. Ch.: Linear finite elements with high accuracy. J. Comput. Math. 3 (1985), 115-133. · Zbl 0577.65094
[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)
[10] Mosco, U.: Convergence of convex sets and of solutions of variational inequalities. Adv. in Math. 3 (1969), 510-585. · Zbl 0192.49101
[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. · Zbl 0302.65085
[12] Zlámal, M.: Curved elements in the finite element method. SIAM J. Numer. Anal. 10 (1973), 229-240. · Zbl 0285.65067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.