Error estimates for some quasi-interpolation operators. (English) Zbl 0938.65125

Verfürth, Rüdiger

M2AN, Math. Model. Numer. Anal. 33, No. 4, 695-713 (1999).

Explicit bounds on the constants for two quasi-interpolation operators which are modifications of the classical Clément-operator is derived. The estimates proposed are crucial for the construction of explicit constants which appear in the commonly used a posteriori error estimates. The obtained results are also compared with corresponding estimates for the standard nodal interpolation operator.

Reviewer: J.Vaníček (Praha)

MSC:

65N15	Error bounds for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

error bounds; quasi-interpolation operators; Clément-operator; a posteriori error estimates; nodal interpolation operator