.. _V1.01.346:

**v1.01.346** ZZZZ346 — Bifurcation of a straight XFEM interface with quadratic 2D elements
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**Summary**

The purpose of this test is to validate the sub-division algorithm XFEM, with quadratic 2D elements. The general subdivision algorithm is described in the reference material [:ref:`R7.02.12 <R7.02.12>`]. Moreover, sub-division occurs mainly when calling the operator MODI_MODELE_XFEM [:ref:`U4.41.11 <U4.41.11>`].

In this test, we are interested in a particular cutting situation: the bifurcation of an interface along an edge, within an element itself. Depending on the position of the bifurcation point on the edge, we have two cutting configurations [:ref:`R7.02.12 <R7.02.12>`]. These configurations correspond to two regularizations of the shape of the level-set.

We are considering 4 models:


1. modeling :math:`A`: :math:`\text{X-FEM}\mathrm{2D}` with TRIA6 elements, the interface bifurcates before the midpoint on the bifurcation edge.


2. modeling :math:`B`: :math:`\text{X-FEM}\mathrm{2D}` with QUAD8 elements, the interface bifurcates before the midpoint on the bifurcation edge.


3. Modeling :math:`C`: :math:`\text{X-FEM}\mathrm{2D}` with TRIA6 elements, the interface bifurcates after the midpoint on the bifurcation edge.


4. modeling :math:`D`: :math:`\text{X-FEM}\mathrm{2D}` with QUAD8 elements, the interface bifurcates after the midpoint on the bifurcation edge.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Synth_ses_des_r_sultats