An extension theorem for equilibrium finite elements spaces (Q1922229)

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.