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J. Melenk, T. Eibner:
"A local error analysis of the boundary concentrated FEM";
IMA J. Numer. Anal., 26 (2006), 4; S. 752 - 778.

The boundary concentrated finite element method is a variant of
the $hp$-version of the FEM that is particularly suited for the
numerical treatment of elliptic boundary value problems with
smooth coefficients and boundary conditions with low regularity or
non-smooth geometries. In this paper we consider the case of the
discretization of a Dirichlet problem with exact solution $u\in
H^{1+\delta}(\W)$ and investigate the local error in various
norms. We show that for a $\beta>0$ these norms behave as
$O(N^{-\delta-\beta})$, where $N$ denotes the dimension of the
underlying finite element space. Furthermore, we present a new
Gauss-Lobatto based interpolation operator that is adapted to
the case non-uniform polynomial degree distributions.