A local projection operator for quadrilateral finite elements

Girault, V.

doi:10.1090/S0025-5718-1995-1308454-X

A local projection operator for quadrilateral finite elements
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Math. Comp. 64 (1995), 1421-1431 Request permission

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

Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
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 applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 409–474. MR 0421108
J. Deny and J. L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 21 (1945), 305–370 (1955) (French). MR 74787
Vivette Girault and Pierre-Arnaud Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, vol. 5, Springer-Verlag, Berlin, 1986. Theory and algorithms. MR 851383, DOI 10.1007/978-3-642-61623-5
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 3, Travaux et Recherches Mathématiques, No. 20, Dunod, Paris, 1970 (French). MR 0291887

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