2. Benchmark solution#

2.1. Calculation method#

The analytical reference solution is given by:

(2.1)#\[ T\ mathrm {=} 100\ mathrm {\ times} ({X} ^ {6} + {Y} ^ {6})\]

The Dirichlet and Neumann conditions and the source term are obtained by the method of manufactured solutions [bib1].

2.2. Reference quantities and results#

The value of the difference between analytical solutions and calculated on the mesh: \(\mathrm{\sum }^{\text{noeuds}n}\mathrm{\mid }{T}_{\text{n}}^{\text{calc}}\mathrm{-}{T}_{\text{n}}^{\text{ref}}\mathrm{\mid }\).

In the case of models that perform a convergence analysis with the fineness of the mesh, the speed of convergence with the fineness of the mesh from the solution calculated 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 where \(C\) is independent of \(h\).

2.3. Uncertainties about the solution#

None

2.4. Bibliographical references#

  1. Document U2.08.08, Using the Manufactured Solutions Method for Software Validation, Code_Aster U2 Documentation