On the error of linear interpolation and the orientation, aspect ratio, and internal angles of a triangle

SIAM Journal on Numerical Analysis

Volumn 43, Issue 1, 2005, Pages 19-40

  Cao, Weiming ^a  

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

Author keywords

Anisotropic mesh; Aspect ratio; Linear interpolation; Maximum angle condition; Mesh alignment

Indexed keywords

ANISOTROPIC MESH; LINEAR INTERPOLATION; MAXIMUM ANGLE CONDITION; MESH ALIGNMENT;

ANISOTROPY; ASPECT RATIO; MATHEMATICAL MODELS; PROBLEM SOLVING;

INTERPOLATION;

EID: 33644529423     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142903433492     Document Type: Article

References (16)

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. R. E. BANK AND R. K. SMITH, Mesh smoothing using a posteriori error estimates, SIAM J. Numer. Anal., 34 (1997), pp. 979-997.
4. M. BERZINS, A solution-based triangular and tetrahedral mesh quality indicator, SIAM J. Sci. Comput., 19 (1998), pp. 2051-2060.
5. J. BRAMBLE AND M. ZLÁMAL, Triangular elements in the finite element method, Math. Comp., 24 (1970), pp. 809-820.
6. E. F. D'AZEVEDO AND R. B. SIMPSON, On optimal interpolation triangle incidences, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 1063-1075.
7. L. FORMAGGIA AND S. PEROTTO, New anisotropic a priori error estimates, Numer. Math., 89 (2001), pp. 641-667.
8. W. HUANG, Measuring mesh qualities and application to variational mesh adaptation, SIAM J. Sci. Comput., 26 (2005), pp. 1643-1666.
9. W. HUANG AND W. SUN, Variational mesh adaptation II: Error estimates and monitor functions, J. Comput. Phys., 184 (2003), pp. 619-648.
10. P. KNUPP, L. G. MARGOLIN, AND M. SHASHKOV, Reference Jacobian optimization-based rezone strategies for arbitrary Lagrange Eulerian methods, J. Comput. Phys., 176 (2002), pp. 93-128.
11. G. KUNERT, A Posteriori Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes, Ph.D. dissertation, TU Chemnitz, Chemnitz, Germany, 1999.
12. E. J. NADLER, Piecewise Linear Approximation on Triangulations of a Planar Region, Ph.D. thesis, Division of Applied Mathematics, Brown University, Providence, RI, 1985.
13. S. RIPPA, Long and thin triangles can be good for linear interpolation, SIAM J. Numer. Anal., 29 (1992), pp. 257-270.
14. J. R. SHEWCHUK, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, Technical report, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 1996.
15. R. B. SIMPSON, Anisotropic mesh transformations and optimal error control, Appl. Numer. Math., 14 (1994), pp. 183-198.
16. L. N. TREFETHEN AND D. BAU, Numerical Linear Algebra, SIAM, Philadelphia, 1997.