An optimally convergent smooth blended B-spline construction for semi-structured quadrilateral and hexahedral meshes

Easy to construct and optimally convergent generalisations of B-splines unstructured meshes are essential for the application isogeometric analysis domains with non-trivial topologies. Nonetheless, especially hexahedral meshes, construction smooth basis functions is still an open question. We introduce a simple partition unity that yields blended B-splines, referred as SB-splines, on semi-structured quadrilateral i.e. mostly structured sufficiently separated regions. To this end, we first define mixed smoothness C 0 continuous in regions mesh but have higher everywhere else. Subsequently, SB-splines obtained by smoothly blending physical space Bernstein bases equal degree. One key novelties our approach required weight assembled from available mesh. The globally smooth, non-negative, no breakpoints within elements reduce conventional away Although consider only quadratic paper, generalises arbitrary degrees. demonstrate excellent performance studying Poisson biharmonic problems numerically establishing their optimal convergence one two dimensions. • A B-spline proposed. Basis bases. Requisite B-splines. Construction permits efficient Gauss–Legendre quadrature integrals. Optimal demonstrated.