Approximation Properties for Blended B-Splines on Unstructured Quadrilateral Mesh

In this paper, the approximation properties for blended B-splines on unstructured quadrilateral mesh are analyzed. It is demonstrated that the blended B-splines can generate bi-cubic polynomials when being applied on regular and irregular elements. Moreover, the construction of dual basis for standard B-splines is extended to blended B-splines and the boundedness of the corresponding linear functional is established. Finally, the blended B-splines exhibit the optimal convergence in both the parametric and physical domains.