Abstract
Throughout the paper, we consider conforming planar triangulations of a given polygon into triangles, i.e., the union of all triangles of any particular triangulation is always equal to the polygon, and any two different triangles in any particular triangulation may only have a common edge, or a common vertex, or no common point (cf. [12]). In most of cases namely such conforming triangulations are used in the finite element modelling and analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. S. Baker, E. Grosse, and C. S. Rafferty, Nonobtuse triangulation of polygons, Discrete Comput. Geom. 3 (1988), 147–168.
R. E. Bank, PLTMG: A Software Package for Solving Partial Differential Equations: Users’ Guide 7.0, SIAM, Philadelphia, 1994.
G. F. Carey, Computational Grids. Generation, Adaptation, and Solution Strategies, Series in Computational and Physical Processes in Mechanics and Thermal Sciences, Taylor & Francis, Washington, DC, 1997.
P. G. Ciarlet, P. A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17–31.
M. Feistauer, J. Felcman, M. Rokyta, and Z. Vläšek, Finite-element solution of flow problems with trailing conditions, J. Comput. Appl. Math. 44 (1992), 131–165.
H. Fujii, Some remarks on finite element analysis of time-dependent field problems, Theory and Practice in Finite element Structural Analysis, Univ. Tokyo Press, Tokyo, 1973, pp. 91–106.
J. L. Gerver, The dissection of a polygon into nearly equilateral triangles, Geom. Dedicata 16 (1984), 93–106.
R. Kornhuber, R. Roitzsch, On adaptive grid refinement in the presence of internal or boundary layers, Impact Comput. Sci. Engrg. 2 (1990), 40–72.
S. Korotov, M. Křížek, Acute type refinements of tetrahedral partitions of polyhedral domains, SIAM J. Numer. Anal. 39 (2001), 724–733.
S. Korotov, M. Křížek, and P. Neittaanmäki, Weakened acute type condition and the discrete maximum principle, Math. Comp. 70 (2001), 107–119.
S. Korotov, J. Stańdo, Yellow-red and nonobtuse refinements of planar triangulations, Math. Notes (Miskolc) 3 (2002), 39–46.
M. Křížek, P. Neittaanmäki, Mathematical and Numerical Modelling in Electrical Engineering: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
M. Křížek, Qun Lin, On diagonal dominancy of stiffness matrices in 3D, East-West J. Numer. Math. 3 (1995), 59–69.
M. Křížek, J. Šolc, Acute versus nonobtuse tetrahedralizations, in: Conjugate Gradients Algorithms and Finite Element Methods, SpringerVerlag, Berlin, 2004, pp. 161–170.
V. Ruas Santos, On the strong maximum principle for some piecewise linear finite element approximate problems of non-positive type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 473–491.
G. Strang, G. J. Fix, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, N. J., 1973.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Korotov, S., Stańdo, J. (2004). Nonstandard Nonobtuse Refinements of Planar Triangulations. In: Křížek, M., Neittaanmäki, P., Korotov, S., Glowinski, R. (eds) Conjugate Gradient Algorithms and Finite Element Methods. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18560-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-18560-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62159-8
Online ISBN: 978-3-642-18560-1
eBook Packages: Springer Book Archive