Dear Irene, do you mean A. the convergence in teh sense of the convergence errors in each step, or B. the global convergence - i.e., as referred in the basic convergence theorem (general for partial differential equation) that approximation + stability gives convergence = approximation of the solution getting closer with mesh refinement? Or something else?

If A., the absolute mesh size is not as important as other factors, like the finite element shapes. If B., I can only rephrase the previous answer: a finer mesh should give results closer to the exact solution of the equations, however, of course getting closer than the errors made in the assumptions applied when fomulating the equatons (e.g., concrete as a homogeneous continuum), has no sense.