2. Principle of the test

We mesh a square (in \(\mathrm{2D}\)) or a cube (in \(\mathrm{3D}\)) using linear elements with straight edges (TRIA3, QUAD4, HEXA8, PENTA6, TETRA4, PYRAM5). The square (or the cube) is meshed twice with different discretizations. Let’s call these 2 meshes MA1 and MA2.

The CREA_MAILLAGE command is used to transform these linear meshes into quadratic meshes (“LINE_QUAD”).

We also use the CREA_MAILLAGE command to create « QUAD + » meshes: QUAD9, HEXA27, and PENTA18.

We then have linear (« LIN »), quadratic (« QUAD ») or « QUAD + » meshes for all types of meshes: TRIA, QUAD,…,…, PYRAM

With the MODI_MAILLAGE/DEFORME command, you can deform meshes MA1 and MA2 so that the edges of the elements become curved.

A node field is then created (CH1) whose form is « analytical » (application of a formula to the coordinates of the nodes of the MA1 mesh). You can use 3 different formulas:

• an affine coordinate function (noted as « degree 1 »)

• a quadratic coordinate function (noted as « degree 2 »)

• any coordinate function (noted « degree 2+ » although fractional powers are actually used).

We then make a projection of CH1 from MA1 to MA2. We get CH2. This field is projected again from MA2 to MA1. We get CH1B.

CH1 and CH1B having the same support mesh, we can then calculate the relative error caused by the double projection.

The « maximum » of the relative error on the mesh is then calculated (and tested).

Note: As the PROJ_CHAMP command is sometimes used between 2 meshes whose nodes are geometrically confused (for example studies THM), we also test this configuration (MA2 = MA1) to verify that in this case, the projection error is zero.