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Table 1 The approximate results for the first derivative

From: A fourth order accurate approximation of the first and pure second derivatives of the Laplace equation on a rectangle

h \(\Vert v-v_{h}\Vert \) \(\Re_{v}^{m}\)
\(\frac{1}{8}\) 2.299996064764325009657E − 2  
\(\frac{1}{16}\) 1.894059104568160525104E − 3 12.14
\(\frac{1}{32}\) 1.344880793701474553783E − 4 14.08
\(\frac{1}{64}\) 8.960663249977644986927E − 6 15.01
\(\frac{1}{128}\) 5.796393863873542692774E − 7 15.46