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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
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