Verification and validation can be thought of as a formal process for checking results. Each of these terms has a specific meaning which we won't get into here. The only verification check discussed below is investigation of the effect of mesh size on the results.
Let's check what happens to the heat flux variation along the bottom surface when we refine the mesh i.e. use more elements in the mesh.
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To resolve the steep temperature gradient at right, lower corner, we bias the edge sizings using the following process demonstrated in the video below:
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We created a third solution instance where we doubled the edge sizings again, keeping the bias factors the same. The following figure shows that the heat flux variation along the bottom surface is almost the same on the two finer meshes (20x40 and 40x80). This demonstrates that the results on the two finest meshes are mesh independent and are likely very close to the exact solution (which could be derived using separation of variables).
The above figure was generated in MATLAB from the Excel file using this MATLAB script. The Excel file called boundary_flux_tutorial.xlsx had four columns as shown below.
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