Consistency and convergence properties of the isogeometric collocation method

• Given a differential operator DD, a NURBS function TrTr and DTrDTr have the same knot intervals.
• The consistency property of the IGA-C method is proved.
• The IGA-C method is convergent if the differential operator is stable or strongly monotone.

Isogeometric collocation (IGA-C) method has shown its superior behavior over Galerkin method in terms of accuracy-to-computational-time ratio and other aspects. However, relatively little has been published about numerical analysis of the IGA-C method. This paper develops theoretical results on consistency and convergence of the IGA-C method to a generic boundary (initial) problem. It shows that the IGA-C method is convergent when differential operator of the boundary (initial) problem is stable or strongly monotone. Finally, we show some concrete examples whose differential operators are strongly monotone, and the IGA-C method is convergent. Moreover, 2D and 3D numerical examples are presented.