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January 16, 2011, 04:37 
How do I apply the L norms?

#1 
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I know this is a real newbie question.
I want to apply the L2norm for a laplace equation. How should I proceed? Should I simply calculate the difference between the values of the current and the last iteration, then the sum of the squares of these values and finally the square root? Is this norm used to determine when to stop iterating? Thanks a lot! 

January 16, 2011, 05:01 

#2 
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January 17, 2011, 06:26 

#3 
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Thanks, that's very interesting!
If I still want to compare the solutions from the latest two iterations, do I have to treat the domensions sepparately or not? Obviusly, by applying a L2norm for a 3D domain will naturally provide higher values than an L2norm for a 1D domain (because will be more points in the grid). Further can you recommend me a good documentation on applying Lnorms in CFD? 

January 19, 2011, 03:31 

#5 
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I'm implementing the basic laplace equation, i.e. the RHS is zero... How should I proceed?
Thanks! 

January 19, 2011, 05:15 

#6 
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If the right hand side is zero, the problem is pretty boring, isn't it? No boundary conditions, no source term?


January 19, 2011, 07:05 

#7 
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Ohh...now I understand, my mistake. The RHS also includes the boundary conditions (which are specified in my problem)...


January 22, 2011, 03:14 
Hi

#8 
Member

Hi
You can use the following norm for stopping your iterations. It just calculates the relative error in the iterations total_error=sqrt((\sun_{j=1}^N(\frac{u^(n+1)  u^(n)}{u^n})^2)_j) which corresponds to all the points in the grid. You can compare this to an epsilon value and if the condition is met the iteration stops. n in the above formula represents the iteration count. 

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