Abstract
In this paper we present one approach to build optimal meshes for P 1 interpolation. Considering classical geometric error estimates based on the Hessian matrix of a solution, we show it is possible to generate optimal meshes in H 1 seminorm via a simple minimization procedure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
1. Alauzet F., Adaptation de maillage anisotrope en trois dimensions. Application aux simulations instationnaire en Mecanique des Fluides, PhD thesis, Universit des Sciences et Techniques du Languedoc, France, 2003.
2. Borouchaki H. and Frey P.J., Adaptive triangular-quadrilateral mesh generation. Int J Numer Meth Engng 41:915–934, 1998.
3. Ciarlet P.G. Introduction à l'analyse numrique matricielle et à l'optimisation, Masson, Paris, 1982.
4. Ciarlet P.G. Basic error estimates for elliptics problems. in Ciarlet P.G., Lions J.-L. (eds), Handbook of numerical analysis, vol II North Holland Amsterdam 1991.
5. Cao W. On the error of linear interpolation and the orientation, aspect ratio, and internal angles of a triangles, SIAM J.Numer. Anal. Vol. 43, No 1, pp. 19–40.
6. Dompierre J., Labb P., Guibault F., Controlling Approximation Error, Second M.I.T Conference on Computational Fluid and Solid Mechanics. Cambridge, Elsevier, p. 1929–1932, 2003.
7. Fortin M. Estimation d'erreur a posteriori et adaptation de maillages, Revue europ é enne des é l é ments finis, 9(4), 2000
8. Fortin M. Anisotropic mesh generation, é cole CEA-INRIA-EDF : A posteriori estimation and output bound computation, 2004.
9. Frey P.J., Borouchaki H. Surface meshing using a geometric error estimator. Int J Numer Meth Engng 58(2):277–45, 2003.
10. Frey P.J. Georges P.-L. Mesh generation. Application to finite elements. Paris, Oxford: Hermes Sciences Publ., 2000.
11. D'Azevedo E., Are Bilinear Quadrilaterals Better Than Linear Triangles? SIAM Journal on Scienti.c Computing Vol. 22, No 1, pp. 198–217.
12. F.Hecht, K.Ohtsuka and 0.Pironneau. FreeFem++ manual Universite Pierre et Marie Curie, http://www.freefem.org/.++/index.htm
13. F.Hecht. A few snags in mesh adaptation loops. In Proc. of 14th Int. Meshing Roundtable, San Diego, USA, 2005
14. Manole C.-M., Vallet M.-G., Dompierre J. and Guibault F. Benchmarking Second Order Derivative Recovery of a Piecewise Linear Scalar Field, Proceedings of the 17th IMACS World congress Scientific Computation, Applied Mathematic and Simulation, 2005.
15. S. Rippa, Minimal rougthness property of the Delaunay triangulation, Comput. Aided Geom Design, 7: pp. 489–497, 1990
16. Vassilevski Yu.V., Lipnikov K.N. Opimal Triangulations: Existence, Approximation, and double differentiation of P 1 Finite Element Functions. Comput. Math. Math. Phys. Vol 43, No 6, 2003, pp. 827–835.
17. Zhang X. D., Accuracy concern for Hessian Metric, Internal note, CERCA, 2001.
18. Zienkiewicz O.C, Zhu J.Z. The superconvergent patch recovery and a posteriori error estimates. Part I: the recovery technique. Int J Numer Meth Engng 33(7):1331–1364, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Lagüe, JF., Hecht, F. (2006). Optimal Mesh for P 1 Interpolation in H 1 Seminorm. In: Pébay, P.P. (eds) Proceedings of the 15th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34958-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-34958-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34957-0
Online ISBN: 978-3-540-34958-7
eBook Packages: EngineeringEngineering (R0)