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How to access the exact solution (Mode analysis)

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Hi everyone,
For mode analysis, by setting the computation domain large enough (i.e. 8 lambda*8 lambda), the obtained results are varied as increasing mesh density, so I am just stuck are there any criteria to judge whether the solution access the exact solution or not? Or can I judge from convergence (for example the convergence value should be smaller than ..)?
Thanks for your assistance.
Regards


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