On the effect of scaled B-splines for different approaches to locally refined splines

Both Truncated Hierarchical B-splines and LR B-splines use scaled B-splines as part of the construction to ensure partition of unity. Certain configurations of refinements have a surprisingly big effect on the scaling factor. As the scaling factors have a direct effect on magnitude of the elements in the mass and stiffness matrices scaling consequently directly impacts the condition numbers of these matrices. The talk addressed how these effects can be observed already for bi-degree (3, 3), and that the effect grows with growing polynomial degrees.