# Calculate accuracy order/rate

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

• Possible duplicate/related: scicomp.stackexchange.com/questions/21295/… – Christian Clason Sep 21 '18 at 14:04
• 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 $e(h) \approx C h^r$? – Wolfgang Bangerth Sep 22 '18 at 1:57
• 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 – Mr. Robot Sep 22 '18 at 3:27
• @Wolfgang yes, that's what I mean – Mr. Robot Sep 22 '18 at 3:36

## 1 Answer

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