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Error decreases in one norm and increases in another one

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Old   October 16, 2013, 07:56
Question Error decreases in one norm and increases in another one
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Dmitry
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Hi everyone!

Have anyone experienced when error decreases in one norm and grows up in another one during convergence study?

In particulary, in L_1 norm error goes down, while goes up in both L_2 and L_infty.
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Old   October 16, 2013, 11:29
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Filippo Maria Denaro
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Originally Posted by odzaru View Post
Hi everyone!

Have anyone experienced when error decreases in one norm and grows up in another one during convergence study?

In particulary, in L_1 norm error goes down, while goes up in both L_2 and L_infty.
That sounds strange....something does not work properly... have you reached a real convergent slope? what about your test?
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Old   October 16, 2013, 12:56
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It is odd that 1-norm and 2-norm behave differently. I would have expected if a norm behaves differently, that would be the max-norm.
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Old   October 16, 2013, 13:43
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I guess, i have found the reason. Briefly speaking, I have unsteady flow of 2D Taylor-Green vortexes and therefore mixed spatial and temporary error. For a fixed grid resolution I performed time step convergence study and observed increase in error in L_2 and L_infty norms, while in L_1 norm the error decreased with almost the expected order.
After the grid was refined, I observed error drop in both L1 and L2 norms, not L_infty. After one more grid refinement, all the norms showed error drop. So probably the spatial error was dominated over the temporary error.
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Old   October 16, 2013, 16:39
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Originally Posted by odzaru View Post
I guess, i have found the reason. Briefly speaking, I have unsteady flow of 2D Taylor-Green vortexes and therefore mixed spatial and temporary error. For a fixed grid resolution I performed time step convergence study and observed increase in error in L_2 and L_infty norms, while in L_1 norm the error decreased with almost the expected order.
After the grid was refined, I observed error drop in both L1 and L2 norms, not L_infty. After one more grid refinement, all the norms showed error drop. So probably the spatial error was dominated over the temporary error.
yes, if you fix thye space grid h then a part of the local truncation error becomes constant and decreasing the time-step under this constant value no longer decreases the error. The convergence study for the temporal accuracy must be done only on the finest spatial grid you can use.
Conversely, the accuracy study done by taking dt/h= constant does not produce such problem.
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Old   October 16, 2013, 20:33
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yes, if you fix thye space grid h then a part of the local truncation error becomes constant and decreasing the time-step under this constant value no longer decreases the error. The convergence study for the temporal accuracy must be done only on the finest spatial grid you can use.
Conversely, the accuracy study done by taking dt/h= constant does not produce such problem.
Thank you, Filippo, I agree with you. I have a confusing situation. My order of spatial discretisation is about one. With this I need to test high order scheme in time. It becomes too heavy to estimate temporary order on very fine grid.
I know a little bit about the second approach of simultaneous grid and time step refinement. Can you suggest any literature about it? Thanks in advance.
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