2. Benchmark solution

2.1. Calculation method

The reference solution is obtained by refining the modeling A mesh (classical axisymmetric elements with mesh crack): regular mesh composed of \(1000\mathrm{\times }2000\) QUAD8 (instead of \(100\times 200\) QUAD8 for mesh A)

2.2. Reference quantities and results

The temperature is tested at the end of the last time step (\(t=1\text{.}s\)) at points \({P}^{\text{+}}(\theta )\) and \({P}^{\text{-}}(\theta )\) (see Figure).

Identification	Reference type	Reference value
Point \({P}^{\text{+}}(\theta )\) - \(\mathit{TEMP}\)	“AUTRE_ASTER”	\(\mathrm{23,559884847913}°C\)
Point \({P}^{\text{+}}(\theta )\) - \(\mathit{TEMP}\)	“AUTRE_ASTER”	\(\mathrm{15,592470476233}°C\)

Since the problem is axisymmetric, the values tested cannot vary with \(\theta\). These values are then tested with:

• \(\theta \mathrm{=}0\) for A and B models (\(\text{FEM AXIS}\) and \(\text{X-FEM AXIS}\) respectively)

• \(\theta \mathrm{=}\pi \mathrm{/}4\) for C and D models (\(\text{FEM 3D}\) and \(\text{X-FEM 3D}\) respectively)