NUMERICAL VERIFICATION
A mesh convergence study that answers the right question
A finer mesh is useful only when you know which quantity must converge.
Choose the quantity first
Define a quantity of interest before changing the mesh: displacement at a specified point, strain energy, a reaction force, or stress along a physical path. Keep the geometry, material, loads and solution settings consistent.
Refine systematically
Run at least three sensible mesh levels. Record the element formulation, number of degrees of freedom and the quantity of interest. Compute the relative change between successive solutions. The tolerance should follow the engineering decision; there is no universal percentage that makes every analysis acceptable.
Watch for singularities
The maximum stress at a point load, sharp re-entrant corner or idealised fixed edge can increase without convergence. Refinement does not fix a singular idealisation. Reconsider the load distribution or geometry, or report a physically justified stress measure away from the singular location.
Check more than the plot
Confirm force and moment balance, units and deformation shape. For nonlinear analyses also assess increments, convergence tolerances and relevant energy measures. Mesh convergence is numerical verification; agreement with representative physical measurements is validation.