Strelkov, N. A. On projection-difference analogues of the identity operator. (English) Zbl 0803.65100 Kowalski, Jan Krzysztof (ed.) et al., Numerical analysis and mathematical modelling. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 29, 227-231 (1994). Author’s summary: It is shown that there exists no finite element subspace of the space \(W_ 2^ 1\) whose approximation properties are optimal with respect to the rate and which generates an analogue of the unit operator with the fivepoint “cross-type” stencil. A full description of the projective-grid analogues of the identity operator is given.For the entire collection see [Zbl 0790.00003]. Reviewer: C.L.Koul (Jaipur) MSC: 65N06 Finite difference methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35J20 Variational methods for second-order elliptic equations Keywords:projection-difference operator; cross-type stencil; finite element PDFBibTeX XMLCite \textit{N. A. Strelkov}, Banach Cent. Publ. 29, 227--231 (1994; Zbl 0803.65100)