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L1 error vs L2 error estimates

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Old   May 12, 2008, 22:14
Default L1 error vs L2 error estimates
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Hi, I am having a basic doubt in error estimates.

If I am right, L1 error is like standard deviation and L2 error is like RMS with the mean value being the analytical soln.

When I test my code, I get improved order of convergence with L2 error when compared to L1 error.

Now, what is the significance of L2 error over L1 error? How to know when to use L1 error and when to use L2 error?

Thanks in advance for your comments.

Regards, Shyam
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Old   May 13, 2008, 02:43
Default Re: L1 error vs L2 error estimates
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Dear Shyam,

The choice of the norm depends on the problem you are looking at. However, L1 and L2 norms are generally known to behave in the same way. There is no specific reason to choose one norm over the other, especially for smooth flow problems where all the norms are equivalent. For a uniform mesh, it is easy to see for youself that the L1 and L2 norms yield the same result. However, a more suitable norm would be to use a volume weighted norm in L1 sense which can be used for all types of meshes and all types of problems. (See "Error localization in solution-adaptive grid methods", Sun & Tkayama, JCP, Sep 2003, pp. 346--350)

Hope this helps



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