Discussion
Consider the following statements about mesh convergence:
1. A single result does not demonstrate accuracy.
2. Convergence should be shown for the quantity of interest.
3. A stress singularity converges once the mesh is fine enough.
Which of the statements given above is or are correct?
Answer: D
Correct answer: 1 and 2 only
Statements 1 and 2 are correct. Statement 3 is the classic trap: at a re-entrant corner or a point load the elasticity solution is genuinely infinite, so the computed stress rises without limit as the mesh is refined and never converges at all. A rising peak stress there is the model working correctly, and the remedy is to model the real fillet radius or to use a different criterion, not to refine further.
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