Abstract
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.
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