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L1 and L-infinite error

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Old   July 18, 2002, 06:27
Default L1 and L-infinite error
  #1
Kenshi Yamashita
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Hi everyone. I am trying to test the accuracy of several schemes with a linear advection test problem. And I want to get eL1 errorf and eL-infinite errorf by comparing numerical solution with analytical one. Can anyone teach me the definition of L1 and L-infinite error. Thanks.
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Old   July 18, 2002, 14:39
Default Re: L1 and L-infinite error
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Junseok Kim
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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
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Old   July 19, 2002, 12:56
Default Re: L1 and L-infinity error
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Kenshi Yamashita
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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
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Old   July 19, 2002, 13:19
Default Re: L1 and L-infinity error
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Junseok Kim
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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

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Old   August 7, 2002, 07:37
Default Re: L1 and L-infinity error
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sulaksana
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L1=sum(abs(Ri)) L-infinity=max(Ri) ; i=1,2,3,.. where R=residual
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