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-   -   L1 and L-infinite error (http://www.cfd-online.com/Forums/main/4944-l1-l-infinite-error.html)

 Kenshi Yamashita July 18, 2002 06:27

L1 and L-infinite error

Hi everyone. I am trying to test the accuracy of several schemes with a linear advection test problem. And I want to get eL1 errorf and eL-infinite errorf by comparing numerical solution with analytical one. Can anyone teach me the definition of L1 and L-infinite error. Thanks.

 Junseok Kim July 18, 2002 14:39

Re: L1 and L-infinite error

L_1 = sum |exact - numerical| from i=1 to N L_infinity = max |exact - numerical| from i=1 to N

If you want to compare with different grids, then multiply grid size in the front and take of space dimentions.

Kim

 Kenshi Yamashita July 19, 2002 12:56

Re: L1 and L-infinity error

Thanks for your reply. What I want to do is convergence study of high order schemes. All of such papers, which I have, show that L_1 error is always smaller than that of L_infinity. But the definition that you wrote seems to be opposite to the results. Maybe L_1 = (sum |exact - numerical|) / (gridsize) is right ??? Thanks

Kenshi

 Junseok Kim July 19, 2002 13:19

Re: L1 and L-infinity error

Yes, you are right.

Some authors divide sum by grid size, some are not becuase if you want to calculate error on single grid size, it doesn't matter, but as you told before, if you want to calculate convergence rate, you need to divide the sum by mesh size so that you can compare the error on the different mesh sizes.

Kim

 sulaksana August 7, 2002 07:37

Re: L1 and L-infinity error

L1=sum(abs(Ri)) L-infinity=max(Ri) ; i=1,2,3,.. where R=residual

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