Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A local projection operator for quadrilateral finite elements

Author: V. Girault
Journal: Math. Comp. 64 (1995), 1421-1431
MSC: Primary 65N30; Secondary 65D32
MathSciNet review: 1308454
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This note studies the approximation error of a local projection operator on polynomials of total degree k defined on quadrilaterals. Among other applications, this projection operator permits to derive easily error estimates for quadrature formulas.

References [Enhancements On Off] (What's this?)

  • [1] R. Adams, Sobolev spaces, Academic Press, New York, 1975. MR 0450957 (56:9247)
  • [2] P. G. Ciarlet, The finite element method for elliptic problems, North-Holland, Amsterdam, 1977. MR 0520174 (58:25001)
  • [3] P. G. Ciarlet and P. A. Raviart, The combined effect of curved boundaries and numerical integration in isoparametric finite element methods, The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations (A. K. Aziz, ed.), Academic Press, New York, 1972, pp. 409-474. MR 0421108 (54:9113)
  • [4] J. Deny and J. L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953-54), 305-370. MR 0074787 (17:646a)
  • [5] V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, Springer Series in Comput. Math., vol. 5, Springer-Verlag, Berlin, 1986. MR 851383 (88b:65129)
  • [6] J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1970. MR 0291887 (45:975)
  • [7] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
  • [8] P. A. Raviart, Méthode des éléments finis, Cours de DEA, Lab. d'Analyse Numérique, Université Pierre et Marie Curie, Paris, 1972.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 65D32

Retrieve articles in all journals with MSC: 65N30, 65D32

Additional Information

Keywords: Isoparametric quadrilateral finite elements, local projections, quadrature formulas
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society