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.


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
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