Fig. 2

B-spline (top row) and Lagrange (bottom row) basis functions of order \(p=2,3\) in a 1D element intersecting \(\Omega \). Note that gradient of the blue B-spline basis functions is \(O(h^{-1}(\frac{\delta }{h})^{p-1})\) within \(\Omega \) while the gradient of Lagrange basis functions is \(O(h^{-1})\) regardless of p. a \(C^1 Q^2\) basis. b \(C^1 Q^2\) gradient. c \(C^2 Q^3\) basis. d \(C^2 Q^3\) gradient. e \(Q^2\) basis. f \(Q^2\) gradient. g \(Q^3\) basis. h \(Q^3\) gradient