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Relèvement polynômial de traces et applications. (Polynomial lifting of traces and applications). (French) Zbl 0707.65077

The authors try to solve the following problem. Let on the edges of a square be specified some polynomials of fixed degree. One searches the compatibility conditions in the corners of the square for these polynomials such that they would be the traces of a polynomial defined on the square and having the same degree for each variable. One searches, too some stability properties for this lifting problem depending on the degree of the polynomials and various norms in Sobolev spaces.
The authors obtain some important results that are useful in numerical analysis of the p-version of finite element and spectral methods. They use them in order to improve error bounds for the pressure which is obtained from the discretization of the Stokes problem by a spectral collocation method.
Reviewer: C.I.Gheorghiu

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65D05 Numerical interpolation
76D07 Stokes and related (Oseen, etc.) flows
35J25 Boundary value problems for second-order elliptic equations
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References:

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