A local error analysis of the boundary-concentrated hp-FEM

^** Email: teibner{at}mathematik.tu-chemnitz.de^*** Email: melenk{at}tuwien.ac.at The boundary-concentrated finite-element method (FEM) is a variantof the hp-version of the FEM that is particularly suited forthe numerical treatment of elliptic boundary value problemswith smooth coefficients and boundary conditions with low regularityor non-smooth geometries. In this paper, we consider the caseof the discretization of a Dirichlet problem with the exactsolution u H¹⁺() and investigate the local error in variousnorms. For 2D problems, we show that the error measured in thesenorms is O(N^––ß), where N denotes thedimension of the underlying finite-element space and ß> 0. Furthermore, we present a new Gauss–Lobatto-basedinterpolation operator that is adapted to the case of non-uniformpolynomial degree distributions.