[Vino]

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.!!!

[duri]

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.

[Vino]

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.

[ImanFarahbakhsh]

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???

[FMDenaro]

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

[Vino]

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