Interpolated profile of the horizontal velocity component u at $x=−0.497$ in the top left spectral element, adjacent to the corner $(x,y)=(−1/2,1/2)$⁠. Symbols denote nodal values computed on a uniform grid of 20 × 20 elements $(•)$ and on a non-uniform grid of 40 × 40 elements refined toward the lid $(×)$⁠. The dashed line is the Lagrange interpolation of the nodal values $(•)$⁠, while the full line represents the leading-order term of an asymptotic expansion of the flow near the singular corner at $(x,y)=(−1/2,1/2)$ (Gupta et al., 1981) plus the interpolated residual flow (see the text).