2. Benchmark solution

2.1. Calculation method used for reference solutions

In such a case, it is not possible to unearth an analytical solution! The reference solution used for the calculations of errors on the arrow and on the potential energy of deformation is in fact an approximate solution obtained after a series of four uniform refinements (on the same mesh but in TRIA6).

This uniform refinement procedure can be driven by a PYTHON loop and the MACR_ADAP_MAIL option UNIFORME operator. The first two models are just an illustration of this functionality.

2.2. Benchmark result

Deformation potential energy	\(\mathrm{=}0.102242J\)
Arrow	\(\mathrm{=}–0.0614777m\)

2.3. Uncertainty about solutions

They are only approximate solutions obtained on a « virtually converged » mesh.

2.4. Bibliographical references

1. 24. DESROCHES « Zhu-Zienkiewicz error estimators in 2D elasticity ». [R4.10.01], 1994.

2. 24. DESROCHES « Residual error estimator ». [R4.10.02], 2000.

3. 15. BOITEAU « Courses and TP Error Indicators & Mesh Adaptation; State of the art and implementation in Code_Aster ». http://www.code‑aster.com/utilisation/formations, 2002., 2002.

4. 15. BOITEAU « FORMA05: Thermo-mechanical adaptive mesh on a cracked cylinder head ». [V6.03.120], 2002.