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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!

Compare this to the analytic solution, and note how it converges on the same line: Image Added
This analytic solution has been derived, and is shown to be: Image Added

With the infinite series coefficient defined as:
Image Added

And the Infinite eigenvalues are defined as:

Image Added

Note that Theta, x, and y defined as dimensionless temperature, x coordinate, and y coordinate respectively. The X and Y were reduced by the width W.

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