On a generalized $L_2$ projection and some related stability estimates in Sobolev spaces

Summary.

In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability of a generalized $L_2$ projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces, the stability of the generalized $L_2$ projection is proved assuming some mesh conditions locally.