# L1 and L-infinite error

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 July 18, 2002, 06:27 L1 and L-infinite error #1 Kenshi Yamashita Guest   Posts: n/a 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.

 July 18, 2002, 14:39 Re: L1 and L-infinite error #2 Junseok Kim Guest   Posts: n/a 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

 July 19, 2002, 12:56 Re: L1 and L-infinity error #3 Kenshi Yamashita Guest   Posts: n/a 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

 July 19, 2002, 13:19 Re: L1 and L-infinity error #4 Junseok Kim Guest   Posts: n/a 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

 August 7, 2002, 07:37 Re: L1 and L-infinity error #5 sulaksana Guest   Posts: n/a L1=sum(abs(Ri)) L-infinity=max(Ri) ; i=1,2,3,.. where R=residual

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