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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

MSC:
65D05 Numerical interpolation
41A05 Interpolation in approximation theory
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