Bicubic spline interpolation in L-shaped domains

Birkhoff and de Boor first posed the question of the existence of a convergent bicubic spline interpolation scheme for non-rectangular domains. In this paper that query is answered affirmatively for L-shaped domains. Specifically, it is shown that ∥sf − f∥= O(hr) where sf is the bicubic spline interpolant associated with a smooth function f, h is the maximum mesh spacing, r − 4 for uniform partitions, and r = 3 for nonuniform partitions.