Anisotropic measures of third order derivatives and the quadratic interpolation error on triangular elements

SIAM Journal on Scientific Computing

Volumn 29, Issue 2, 2007, Pages 756-781

  Cao, Weiming ^a  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

Anisotropic mesh; Anisotropic ratio; Aspect ratio; Mesh alignment; Quadratic interpolation

Indexed keywords

ASPECT RATIO; INTERPOLATION; NUMERICAL METHODS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

ANISOTROPIC MESH; ANISOTROPIC RATIO; MESH ALIGNMENT; QUADRATIC INTERPOLATION;

ERROR ANALYSIS;

EID: 41449085933     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050634700     Document Type: Article

References (20)

1. T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., Teubner, Stuttgart, 1999.
2. I. BABUŠKA AND A. K. AZIZ, On the angle condition in the finite element method, SIAM J. Numer. Anal., 13 (1976). pp. 214-226.
3. H. BOROUCHAKI, P. L. GEORGE, F. HECHT, P. LAUG, AND E. SALTEL, Delaunay mesh generation governed by metric specifications. I. Algorithms. Finite Elem. Anal. Des., 25 (1997), pp. 61-83.
4. H. BOROUCHAKI. P. L. GEORGE, AND B. MOHAMMADI, Delaunay mesh generation governed by metric specifications. II. Applications. Finite Elem. Anal. Des., 25 (1997), pp. 85-109.
5. W. CAO, W. HUANG, AND R. D. RUSSELL, A study of monitor functions for two-dimensional adaptive mesh generation, SIAM J. Sci. Comput., 20 (1999), pp. 1978-1994.
6. W. CAO, On the error of linear interpolation and the orientation, aspect ratio, and internal angles of a triangle, SIAM J. Numer. Anal., 43 (2005), pp. 19-40.
7. 2 based on anisotropic measures of higher order derivatives, Math. Comp., to appear.
8. p-norm, Math. Comp., 76 (2007), pp. 179-204.
9. L. CHEN AND J. XU, Optimal Delaunay triangulations, J. Comput. Math., 22 (2004), pp. 299-308.
10. P. G. C'IARLET, The Finite Element Methods for Elliptic Problems, Classics Appl. Math. 40, SIAM, Philadelphia, 2002.
11. E. F. D'AZEVEDO, Optimal triangular mesh generation by coordinate transformation, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 755-786.
12. E. F. D'AZEVEDO AND R. B. SIMPSON, On optimal triangular meshes for minimizing the gradient error, Numer. Math., 59 (1991), pp. 321-348.
13. L. FORMAGGIA AND S. PEROTTO, New anisotropic a priori error estimates, Numer. Math., 89 (2001), pp. 641-667.
14. W. HUANG, Measuring mesh qualities and application to variational mesh adaptation, SIAM J. Sci. Comput., 26 (2005), pp. 1643-1666.
15. W. HUANG AND W. SUN, Variational mesh adaptation II: Error estimates and monitor functions, J. Comput. Phys., 184 (2003), pp. 619-648.
16. E. J. NADLER, Piecewise Linear Approximation on Triangulations of a Planar Region, Ph.D. thesis, Division of Applied Mathematics, Brown University, Providence, RI, 1985.
17. S. RIPPA, Long and thin triangles can be good for linear interpolation, SIAM J. Numer. Anal., 29 (1992), pp. 257-270.
18. J. R. SHEWCHUK, What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measure, in Proceedings of the 11th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, NM, 2002, pp. 115-126.
19. R. B. SIMPSON, Anisotropic mesh transformations and optimal error control, Appl. Numer. Math., 14 (1994), pp. 183-198.
20. M. A. TAYLOR, B. A. WINGATE, AND R. E. VINCENT, An algorithm for computing Fekete points in the triangle, SIAM J. Numer. Anal., 38 (2000), pp. 1707-1720.