Table 1 The 15 best combinations of scaling (\(w_u\) and \(w_p\)) and offset parameters (\(b_u\) and \(b_p\)) for \(\alpha =\beta =1\), based on the \({\mathscr {L}}_2\) relative error.
\(w_u\) | \(w_p\) | \(b_u\) | \(b_p\) | \({\mathscr {L}}_2\) rel. err. | max(abs(\(u-\hat{u}\))) | max(abs(\(p-\hat{p}\))) |
|---|---|---|---|---|---|---|
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}5\) | \(1\textrm{e}{-}4\) | \(1.00\textrm{e}{-}2\) | \(2.54\textrm{e}{-}4\) | \(1.34\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}1\) | \(1.11\textrm{e}{-}2\) | \(2.27\textrm{e}{-}4\) | \(1.77\textrm{e}{-}3\) |
\(1\textrm{e}{-}3\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}5\) | \(1\textrm{e}{-}5\) | \(1.14\textrm{e}{-}2\) | \(2.64\textrm{e}{-}4\) | \(1.76\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}5\) | \(1\textrm{e}{-}1\) | \(1.15\textrm{e}{-}2\) | \(2.73\textrm{e}{-}4\) | \(1.37\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}4\) | \(1\textrm{e}{-}5\) | \(1.15\textrm{e}{-}2\) | \(4.41\textrm{e}{-}4\) | \(1.57\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}4\) | \(1\textrm{e}{-}2\) | \(1.18\textrm{e}{-}2\) | \(2.93\textrm{e}{-}4\) | \(1.50\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1.20\textrm{e}{-}2\) | \(5.12\textrm{e}{-}4\) | \(1.55\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}2\) | \(1.22\textrm{e}{-}2\) | \(5.57\textrm{e}{-}4\) | \(1.47\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}5\) | \(1\textrm{e}{-}5\) | \(1.22\textrm{e}{-}2\) | \(4.52\textrm{e}{-}4\) | \(1.71\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}1\) | \(1.22\textrm{e}{-}2\) | \(3.57\textrm{e}{-}4\) | \(1.29\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}3\) | \(1.24\textrm{e}{-}2\) | \(2.64\textrm{e}{-}4\) | \(1.60\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}4\) | \(1\textrm{e}{-}4\) | \(1.24\textrm{e}{-}2\) | \(2.92\textrm{e}{-}4\) | \(1.83\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1\textrm{e}{-}2\) | \(1.25\textrm{e}{-}2\) | \(3.27\textrm{e}{-}4\) | \(1.64\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}1\) | \(1.26\textrm{e}{-}2\) | \(7.50\textrm{e}{-}4\) | \(1.39\textrm{e}{-}3\) |
\(1\textrm{e}{-}2\) | \(1\textrm{e}{-}3\) | \(1\textrm{e}{-}4\) | \(1\textrm{e}{-}1\) | \(1.27\textrm{e}{-}2\) | \(4.92\textrm{e}{-}4\) | \(1.55\textrm{e}{-}3\) |
