Advances in Continuous and Discrete Models

Theory and Modern Applications

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

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