Mathematical analysis for quadrilateral rotated Q1 element II: Poincare inequality and trace inequality

Journal of Computational Mathematics

Volumn 21, Issue 3, 2003, Pages 277-286

  Ming, Ping Bing ^a   Shi, Zhong Ci ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Poincare inequality; Quadrilateral rotated Q1 element; Trace inequality

Indexed keywords

POLYNOMIALS;

ARBITRARY QUADRILATERAL MESHES; POINCARE INEQUALITY; QUADRILATERAL ROTATED Q ELEMENT; TRACE INEQUALITY;

MATHEMATICAL TRANSFORMATIONS;

EID: 0141963812     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. D.N. Arnold, L.R. Scott and M. Vogelius, Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygonal domain, Ann. Scuola Norm. Sup. Pisacl. Sci-serie, IV XV (1989), 169-192.
2. 1 functions, preprint, 2002.
3. P.G. Ciarlet, Finite Element Methods for the Elliptic Problem, North-Holland, 1978.
4. J. Douglas, J.J. Santos, D. Sheen and X. Ye, Nonconforming Galerkin methods based on quadrilateral elements for the second order elliptic problem, RA1RO, Math. Model and Numer. Anal., 55(1999), 447-470.
5. P. Grisvard, Elliptic Problems in Nonsmooth Domain., Pitman, Boston, 1985.
6. P. Kloucek, B. Li and M. Luskin, Analysis of a class of nonconforming finite elements for crystalline microstructures, Math. Compt., 65 (1996), 1111-1135.
7. B. Li and M. Luskin, Nonconforming finite element approximation of crystalline microstructures, Math. Compt., 67(1998), 917-946.
8. P.-B. Ming, Nonconforming element vs locking problem, PhD. Dissertation, Institute of Computational Mathematics, GAS, 1999.
9. P.-B. Ming and Z.-C. Shi, Convergence analysis for quadrilateral rotated Qi element, in Advances in Computation: Theory and Practice, Vol 7: Scientific Computing and Applications, pp. 115-124. eds: Peter Minev and Yanping Lin, Nova Science Publishers, Inc, 2001,
10. P.-B. Ming and Z.-C. Shi, Quadrilateral mesh revisited, Computer Methods in Applied Mechanics and Engineering., 191 (2002), 5671-5682.
11. J. Necas, Les Methodes Directes en Theorie des Equations Elliptiques, Masson, Paris, 1967.
12. R. Rannacher and S. Turek, A simple nonconforming quadrilateral Stokes element, Numer. Meth. for PDEs., 8 (1992), 97-111.
13. Z.-C. Shi, A convergence condition for the quadrilateral Wilson element, Numer. Math., 44 (1984), 349-361.
14. F. Stummel, Basic Compactness properties of nonconforming and hybrid finite element spaces, RAIRO Anal. Numer., 14 (1980), 81-115.
15. R. Teman, Navier-Stokes Equations, North-Holland, 1983.