I have learned a few ways to improve the accuracy of the solution other than just increasing the mesh size. Here are they:

1. Decrease relative tolerance ~ usually in 10^-5.

2. Increase iterative refinements

3. Use different solver with 2 level solutions improves a lot

4. If u are using a time-dependent study ~ change the time taken by the solver ~ take time steps restricted to some min value or choose intermediate steps.

5. Don't use anything like andersan acceleration to get the convergence earlier.

6. Termination technique in solver ~ use solution + tolerance based ~ NOT the iterations based.

7. Play with scaled option ~ rather automatic use a defined value ~ normally its the max possible (usually if ur soln doesn't converge it is the best way to normalize the variables that are being solved).

If u know more please do share.

Cheers!