Convergence

Convergence is how you know a FEM result can be trusted. There are two distinct kinds: mesh convergence (does refining the mesh still change the result?) and solver convergence (did the iterative solver actually find equilibrium?).

Mesh convergence

FEM is an approximation. On a coarse mesh the result is far from the exact solution; as the mesh is refined the result approaches the true answer. A result is mesh-converged when further refinement no longer changes it meaningfully.

You do not perform this refinement by hand. You state how accurate the answer needs to be, an accepted relative error on the quantity you care about, and Dr.Q runs an automatic h-adaptive convergence study: it refines the mesh itself, concentrating elements where they most reduce the error, and stops once your target is met. The default element is the quadratic tetrahedron. For how to drive that study and read its result, see Mesh Convergence; for the cost of a tight target, see Compute Time & Memory.

When a quantity will not converge

If a stress keeps growing without limit as the mesh is refined, the result is not converging to anything: it is a singularity, and that value is not physical. Refinement never helps there. See Singularities.

Solver convergence

For nonlinear analyses (contact, plasticity, large deformation), the solver iterates to find equilibrium. Each iteration reduces the residual, the out-of-balance force between internal and external loads, and the solver converges when the residual drops below a tolerance.

A nonlinear analysis that reports "converged" is not automatically correct: check that the residual is genuinely below tolerance and that the deformed shape makes physical sense. When the solver fails to converge, see Nonlinear Convergence Errors.