L0, L1, L2 ,Linf error norms
 

Hi,

1)can some one suggest me how to calculate the L0, L1, L2 ,Linf error norms for a 2d case (eg:100X100 grids)?
2) To calculate norms, what are all needed for a steady/unsteady problem?
3) For example, i am solving a incompressible flow over cylinder problem for steady and unsteady, how to generate above said error norms for this problem?

Thanks in advance.!!!

If you want to calculate Ln (nth norm) of a vector, then formula is nth root of( a1^n + a2^n ... + ap^n). Where p is the vector size.
In CFD, residuals are estimated as average over the grid points. L2 norm is equivalent to RMS. Eg., to calculate T residual (temperature) then it is sqrt((T1^2 + T2^2 .. + Tn^2)/n). where n is cell or node count and T1 is (new T - old T) at cell 1.
L1 is equivalent to average of abs(T) residual on the mesh. Linf is the max T residual on the mesh. L0 is number of non-zero elements, I wonder why do you need this norm in residual.

I have lot of confusion in this.... yes. Residual is to check the convergence of the steady state problem (What u have told based on T is a L2 norm???) . Can we use any other norms in residual calculation? In case of unsteady problem, how to check the error or how to check the convergence ? please clarify

Thanks.

Norm
 

I wrote it in Latex syntax
error is a vector with m components then
norm of order nth (L_n) can be defined as
L_n(error)=(\Sigma_i=1^m{{e_i}^n})^{1/n}

Also L_0 is nonsense???

pointwise o averaged Holder norms? You can see the topi in a book of numerical analysis, also the LeVeque book is good

I will check in Leveque book... thanks for your clarification....