L1 and Linfinite 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 errorf and eLinfinite errorf by comparing numerical solution with analytical one. Can anyone teach me the definition of L1 and Linfinite error. Thanks.

Re: L1 and Linfinite 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 
Re: L1 and Linfinity 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 
Re: L1 and Linfinity 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 
Re: L1 and Linfinity error
L1=sum(abs(Ri)) Linfinity=max(Ri) ; i=1,2,3,.. where R=residual

All times are GMT 4. The time now is 19:28. 