Approximation Properties for Blended B-Splines on Unstructured Quadrilateral Mesh

Abstract

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.

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature