Buffa, AnnalisaSangalli, GiancarloSchwab, Christoph2017-04-032017-04-032017-04-03201410.1007/978-3-319-01601-6_15https://infoscience.epfl.ch/handle/20.500.14299/136317We establish exponential convergence of the hp-version of isogeometric analysis for second order elliptic problems in one spacial dimension. Specifically, we construct, for functions which are piecewise analytic with a finite number of algebraic singularities at a-priori known locations in the closure of the open domain Ω of interest, a sequence.(∏<inf>σ</inf>ℓ)ℓ≥0 of interpolation operators which achieve exponential convergence. We focus on localized splines of reduced regularity so that the interpolation operators(∏<inf>σ</inf>ℓ)ℓ≥0 are Hermite type projectors onto spaces of piecewise polynomials of degree p ℓ whose differentiability increases linearly with p. As a consequence, the degree of conformity grows with N, so that asymptotically, the interpoland functions belong to Ck.(Ω) for any fixed, finite k. Extensions to two- and to three-dimensional problems by tensorization are possible. © Springer International Publishing Switzerland 2014.text::book/monograph::book part or chapter