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I replicated Figure 7 of the paper “Static response of miniature capacitive pressure sensors with square or rectangular silicon diaphragm” by G. Blasquez, Y. Naciri, P. Blondel, N. Ben Moussa and P. Pons. We can conclude from the figure that square sensors are more sensitive devices.

Response of square and rectangular sensors

Figure by LauraMabel	Figure from the paper

I numerically computed the first derivative of the following function at interior points using different methods, in an uniform grid of points. Also, I found the average of the absolute error of the predicted first derivative for all the interior points, providing the best prediction.

• Piecewise quadratic spline functions that represent the function
• 1st order forward scheme
• 2nd central difference
• Padé approximation

Plot of results for each approach along with the exact solution.