The boundary-concentrated finite-element method (FEM) 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 the exact solution uH1+δ(Ω) and investigate the local error in various norms. For 2D problems, we show that the error measured in these norms is O(Nδβ), where N denotes the dimension of the underlying finite-element space and β > 0. Furthermore, we present a new Gauss–Lobatto-based interpolation operator that is adapted to the case of non-uniform polynomial degree distributions.

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