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I was doing error analysis of numerical scheme and I get $L_1$ error for each grid size with $N$ element. I was searching reference to compute accuracy order/rate from that error data but doesn't find any good reference. Anyone know?

Error: $e=|u-u_{exact}|$

$L_1$ error: $L_1=1/N \sum_{i=1}^{N} e_i$

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    $\begingroup$ Possible duplicate/related: scicomp.stackexchange.com/questions/21295/… $\endgroup$
    – Christian Clason
    Sep 21, 2018 at 14:04
  • $\begingroup$ It's not quite clear to me what you are asking. Are you saying that you have computed $e(h)$, the $L_1$ error as a function of the mesh size $h$ for several values of $h$, and that you then want to find $C,r$ so that $e(h) \approx C h^r$? $\endgroup$
    – Wolfgang Bangerth
    Sep 22, 2018 at 1:57
  • $\begingroup$ I have test my numerical methods with different grid size, coarse to fine grid. What I asked is how to calculate the rate/order like mentioned this link (see table). scicomp.stackexchange.com/q/19746/28714 $\endgroup$
    – Mr. Robot
    Sep 22, 2018 at 3:27
  • $\begingroup$ @Wolfgang yes, that's what I mean $\endgroup$
    – Mr. Robot
    Sep 22, 2018 at 3:36

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After read some new reference, using first order interpolation, accuracy order/rate simply calculated as follow:

$Order=\frac{log(e_1/e_2)}{log(h_1/h_2)}$

That's it

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