4. B modeling

4.1. Characteristics of modeling

We use a PLAN model.

4.2. Characteristics of the mesh

A convergence study is carried out with the fineness of the mesh from the calculated solution to the analytical solution. A series of meshes obtained by uniform refinement using the MACR_ADAP_MAIL command is used:

• mesh 0:4 SEG3, 2 TRIA6

• mesh 1:8 SEG3, 8 TRIA6

• mesh 2:16 SEG3, 32 TRIA6

• mesh 3:32 SEG3, 128 TRIA6

4.3. Tested sizes and results

The convergence speed is tested with the fineness of the mesh from the calculated solution to the analytical solution in standard \({L}_{2}\), i.e. the greatest real \(\alpha >0\) such as \({\mathrm{\parallel }{T}^{\text{calc}}\mathrm{-}{T}^{\text{ref}}\mathrm{\parallel }}_{\mathrm{0,}\Omega }<C\mathrm{\times }{h}^{\alpha }\) where \(C\) is independent of \(h\).

The sum of the absolute values of the difference between the calculated solution and the analytical solution is also tested.

Identification	Reference type	Reference value
\(\sum ^{\text{noeuds}n}\mid {T}_{\text{n}}^{\text{calc}}-{T}_{\text{n}}^{\text{ref}}\mid\)	“NON_REGRESSION”	0.59734630434863
\(\alpha\)	“ANALYTIQUE”	3.0