First- vs Second-Order Elements — FEA Best-Practice Guide
When higher-order elements help accuracy and when they introduce cost or other problems — reduced versus full integration, and the trade-offs involved.
Principle
Higher-order elements are not automatically better. They increase cost, can introduce convergence difficulties in contact, and may not improve the result if the limiting error is elsewhere (geometry, boundary conditions, material data).
Why it matters
Second-order elements can represent curved geometry and quadratic stress distributions more accurately than first-order elements. However, they roughly double the cost per element and can cause contact convergence issues due to the quadratic contact pressure distribution. In many practical cases, the additional accuracy is below the uncertainty from other modelling assumptions.
Good practice
| Aspect | First-Order (C3D8R) | Second-Order (C3D20R) |
|---|---|---|
| Cost | Low (8 nodes) | High (20 nodes) |
| Bending accuracy | Good (reduced integration) | Excellent |
| Stress gradient capture | Linear | Quadratic |
| Contact | Robust | Can be problematic (pressure oscillation) |
| Hourglassing | Risk (reduced integration) | No hourglassing |
| Geometry curvature | Poor (linear edges) | Good (quadratic edges) |
Warning signs
- Second-order elements used in contact with penalty method — contact pressure can oscillate
- First-order fully integrated elements in bending — shear locking gives artificial stiffness
- Second-order elements used where geometry is meshed linearly anyway — no benefit
- Reduced-integration first-order elements used without hourglass control — zero-energy modes
Verification checks
- Compare first-order and second-order results at the same mesh density — if the difference is small, the extra cost is not justified
- Check hourglass energy in explicit dynamics — should be < 5% of internal energy
- For contact: verify smooth contact pressure distribution with the chosen element order