-2
$\begingroup$

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

|cite|improve this question
$\endgroup$
  • 1
    $\begingroup$ Possible duplicate/related: scicomp.stackexchange.com/questions/21295/… $\endgroup$ – Christian Clason Sep 21 '18 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 '18 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 '18 at 3:27
  • $\begingroup$ @Wolfgang yes, that's what I mean $\endgroup$ – Mr. Robot Sep 22 '18 at 3:36
0
$\begingroup$

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

|cite|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.