Mesh Convergence
How Dr.Q's automatic convergence study decides your mesh is fine enough, and how you steer it.
Mesh convergence answers the question: is the mesh fine enough that the result would not change meaningfully if it were refined further? In Dr.Q you do not chase this by hand. You state an accepted error, and an automatic study refines the mesh until it is met.
How the automatic study works
You define a Question, the quantity you care about (a peak stress, a maximum displacement) together with an accepted relative error. Dr.Q then runs an h-adaptive convergence study: starting from a coarse mesh, it estimates the discretization error, refines where refinement most reduces it, and repeats until the estimated error is within your target. The element type is the quadratic tetrahedron by default. You set the target; the refinement is automatic.
For non-stress-like quantities the study additionally applies Richardson extrapolation internally to sharpen the error estimate. This too is automatic, with nothing to configure.
What "converged" means per quantity
Different quantities converge at different rates, so a sensible accepted error depends on what you are reading:
| Quantity | Typical accepted error |
|---|---|
| Maximum stress | < 5% |
| Maximum displacement | < 2% |
Stresses converge slowest, because they are derived from displacement gradients, so they usually set the pace of the study.
Choosing your target: accuracy vs effort
A tighter target costs disproportionately more compute (see Compute Time & Memory). Match the target to the purpose:
| Goal | Accepted error | Typical cost |
|---|---|---|
| Concept study | ±20–30% | quick |
| Design validation | ±5–10% | moderate |
| Certification | < 1% | full study |
Singularities never converge: stress at a sharp corner keeps growing with refinement, so no target is ever reached there. If the study reports a singularity, add a fillet or read the result away from the point. See Singularities.