Create an optimal mesh with enough precision?

I development a software for optimizing the flat surface grinding.
I create a mesh to calculate my Finite Elements and the numerical results are very good with the analytical solutions and experimental data.
My question is that perphaps I create a mesh with too many elements and I try to look for a mesh with enough precision to calculate the results with the same precision (or more or less a 1% of the desviation) to optimize the calculus time.
What would be the best strategy for doing a convergence analysis?
If anyone need an example please tell me!