Flexible piecewise approximations based on partition of unity

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.AMS subject classification 65N30, 65D05Weimin Han: Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781.Wing Kam Liu: The work of this author was supported by NSF.