Mesh Quality
What makes a good FEM mesh — skewness, aspect ratio, and Jacobian explained.
Mesh quality directly affects result accuracy. Highly distorted elements produce inaccurate results and can cause solver failures.
Key quality metrics
Skewness
Skewness measures how far an element deviates from its ideal shape (equilateral triangle for Tet, cube for Hex). Values range from 0 (perfect) to 1 (completely degenerate).
| Skewness | Quality | | --- | --- | | 0.0 – 0.25 | Excellent | | 0.25 – 0.5 | Good | | 0.5 – 0.75 | Acceptable | | > 0.75 | Poor — may cause inaccuracy |
Aspect ratio
The ratio of the longest to the shortest edge of an element. Ideally close to 1.
- Values up to 5 are generally acceptable
- Values above 10 indicate elongated elements that can produce stress errors
- Thin-section regions naturally produce higher aspect ratios
Jacobian determinant
The Jacobian measures the local mapping between the element coordinate system and the physical space. All values must be positive — negative Jacobian values indicate inverted elements, which cause the solver to fail.
A mesh with any inverted elements (negative Jacobian) cannot be solved. Re-mesh with a coarser or more uniform element size and resolve the geometry defects that caused the inversion.
What causes poor mesh quality?
- Very thin or sliver faces in the geometry
- Sharp re-entrant corners (< 10°)
- Aspect ratio mismatch between adjacent regions
- Extremely small features relative to the overall part size
Improving mesh quality
- Simplify the geometry — remove features smaller than the target mesh size
- Use local mesh refinement rather than globally fine meshes
- Add fillets to sharp corners
- Re-export the geometry after geometry cleanup in the CAD system