×

zbMATH — the first resource for mathematics

Estimations des erreurs de meilleure approximation polynomiale et d’interpolation de Lagrange dans les espaces de Sobolev d’ordre non entier. (Estimation of the best polynomial approximation error and the Lagrange interpolation error in fractional-order Sobolev spaces). (French) Zbl 0587.41018
Explicit bounds for the best polynomial approximation error, explicit and non-explict bounds for the Lagrange interpolation error are derived for functions belonging to fractional order Sobolev spaces defined over a bounded open set in \({\mathbb{R}}^ n\). Thus the classical results of the integer order Sobolev spaces are extended.

MSC:
41A50 Best approximation, Chebyshev systems
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Adams, R.A.: Sobolev spaces. New York: Academic Press 1975 · Zbl 0314.46030
[2] Adams, R.D., Aronszajn, N., Smith, K.T.: Theory of Bessel potentials part II. Ann. Inst. Fourier, Grenoble,17, 1-135, (1967) · Zbl 0185.19703
[3] Arcangeli, R., Gout, J.L.: Sur I’évaluation de I’erreur d’interpolation de Lagrange dans un ouvert de ? n . R.A.I.R.O. Anal. Numer.10, 5-27 (1976) · Zbl 0337.65008
[4] Bramble, J.H., Hilbert, S.R.: Estimation of Linear Functional on Sobolev Spaces with Applications to Fourier Transforms and Spline Interpolation. S.I.A.M. J. Numer. Anal.7, 112-124 (1970) · Zbl 0201.07803 · doi:10.1137/0707006
[5] Bramble, J.H., Hilbert, S.R.: Bounds for a Class of Linear Functionals with Applications to Hermite Interpolation. Numer.Math.16, 362-369 (1971) · Zbl 0214.41405 · doi:10.1007/BF02165007
[6] Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Amsterdam: North Holland 1978 · Zbl 0383.65058
[7] Ciarlet, P.G., Raviart P.A.: General Lagrange and Hermite Interpolation in ? n with Application to Finite Element Methods. Arch. Rat. Mech. Anal.46, 177-199 (1972) · Zbl 0243.41004 · doi:10.1007/BF00252458
[8] Ciarlet, P.G., Wagschal, C.: Multipoint Taylor Formulas and Applications to Finite Element Method. Numer. Math.17, 84-100 (1971) · Zbl 0199.50104 · doi:10.1007/BF01395869
[9] Dupont, T., Scott, R.: Polynomial Approximation of Functions in Sobolev Spaces. Math. Comput.34, 441-463 (1980) · Zbl 0423.65009 · doi:10.1090/S0025-5718-1980-0559195-7
[10] Gout, J.L.: Thèse, Pau (1980)
[11] Grisvard, P.: Commutativité de deux foncteurs d’interpolation et applications. J. Math. Pures Appl.45, 143-290 (1966) · Zbl 0173.15803
[12] Grisvard, P.: Behaviour of the Solutions of an Elliptic Boundary Value Problem in a Polygonal or Polyhedral Domain Numerical Solution of Partial Differential Equations III, Synspade 1975. Hubbard, B., (ed.). Academic Press. New York, 207-274 (1976).
[13] Lions, J.L., Magenes, E.: Problèmes aux limites non homogènes et applications t. I, Dunod, Paris (1968) · Zbl 0165.10801
[14] Lions, J.L., Peetre, J.: Sur une classe d’espaces d’interpolation. Publications Mathématiques de I’I.H.E.S., Paris,19, 5-68 (1964) · Zbl 0148.11403
[15] Meinguet, J.: Structure et estimations de coefficients d’erreurs. R.A.I.R.O. Anal. Numer.11, 355-368 (1977) · Zbl 0399.65076
[16] Ne?as, J.: Les méthodes directes en théorie des équations elliptiques. Paris: Masson 1967
[17] Peetre, J.: Espaces d’interpolation et théorème de Soboleff. Ann. Inst. Fourier, Grenoble,16, 279-317 (1966) · Zbl 0151.17903
[18] Sanchez, A.M.: Thèse de 3 ème cycle, Pau (1984)
[19] Scott, R.: Applications of Banach Spaces Interpolation to Finite Element Theory, preprint (1978)
[20] Strang, G.: Approximation in the Finite Element Method, Numer. Math.,19, 81-98 (1972) · Zbl 0221.65174 · doi:10.1007/BF01395933
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.