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In other words, Always do mesh refinements until the solution converges. If you don't, it is possible your simulation may be completely off from reality, and will be useless!

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https://confluence.cornell.edu/download/attachments/146918522/Convergence.png

Compare this to the analytic solution, and note how it converges on the same line:

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This analytic solution has been derived, and is shown to be:

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