Finite element interpolation of nonsmooth functions satisfying boundary conditions. (English) Zbl 0696.65007

The authors propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. They are preoccupated to define interpolators for “rough functions” and to preserve piecewise polynomial boundary conditions and the approximated functions are averaged appropriately either on d- or (d- 1)-simplices to generate nodal values for the interpolation operator. Optimal estimates for the projection errors are studied.
Reviewer: M.Gaspar


65D05 Numerical interpolation
41A05 Interpolation in approximation theory
Full Text: DOI


[1] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. · Zbl 0314.46030
[2] Douglas N. Arnold, L. Ridgway Scott, and Michael Vogelius, Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 2, 169 – 192 (1989). · Zbl 0702.35208
[3] Philippe G. Ciarlet, The finite element method for elliptic problems, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. · Zbl 0383.65058
[4] Ph. Clément, Approximation by finite element functions using local regularization, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. \jname RAIRO Analyse Numérique 9 (1975), no. R-2, 77 – 84 (English, with Loose French summary). · Zbl 0368.65008
[5] Todd Dupont and Ridgway Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), no. 150, 441 – 463. · Zbl 0423.65009
[6] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. · Zbl 1225.35003
[7] P. Saavedra and L. R. Scott, A variational formulation of free boundary problems, submitted to Math. Comp. · Zbl 0743.65097
[8] S. Zhang, Multi-level iterative techniques, thesis, Pennsylvania State University, 1988.
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.