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An extension theorem for equilibrium finite elements spaces. (English) Zbl 0860.65115

A discrete extension theorem for the equilibrium finite elements spaces is proved. This extension can be used, for example, to estimate the rate of convergence of various domain decomposition algorithms or to study a mortar elements method in equilibrium and mixed formulations.
In the paper some results of functional analysis are introduced, which are used to define the interpolation operator of equilibrium velocity space in noninteger like Sobolev spaces, and the proof of the extension theorem is given.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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