Benchmark solution
=====================


Calculation method
-----------------

No regression.


Reference quantities and results
------------------------

The results of modeling B (mesh method) are taken as a reference.

For B and C models, we check the non-regression of the code with respect to the position of the crack bottom.

For the A, D, E and F models, we check that the nodes closest to the crack bottom trace on plane :math:`(\mathrm{1,}y,z)` at the last moment of propagation have their level-sets very close to zero.


+--------------------------+----------------------+------------------------------+------------------------------+
|**Instant of propagation**|**Knot**              |**Coordinate** :math:`{y}_{i}`|**Coordinate** :math:`{z}_{i}`|
+--------------------------+----------------------+------------------------------+------------------------------+
|3                         |:math:`\mathit{N926}` |2.33                          |8.80                          |
+                          +----------------------+------------------------------+------------------------------+
|                          |:math:`\mathit{N1028}`|2.33                          |9.00                          |
+                          +----------------------+------------------------------+------------------------------+
|                          |:math:`\mathit{N1130}`|2.33                          |9.20                          |
+--------------------------+----------------------+------------------------------+------------------------------+

These nodes are those included in a capture radius equal to the largest edge of an element, centered on the trace of the crack bottom on plane :math:`(\mathrm{1,}y,z)`.

These nodes are identified in the B modeling .mess and the value of their level-sets is estimated in the A, D, E, and F models.