L1 and L-infinite error

July 18, 2002, 06:27

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.

July 18, 2002, 14:39

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

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

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

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

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 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.

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