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.

• Type: Journal
• Year: 2005
• Where: ADCM
• Authors: Weimin Han, Wing Kam Liu
• Keywords: ADCM 2005, Approximations, Flexible Piecewise Approximation, Polynomial Reproducing Conditions