Reference problem
=====================


Geometry
---------

The part considered in both models is a unique element.

Since the temperature is homogeneous in the element, the calculation can be considered as 0D.


Material properties
----------------------


.. csv-table::

    ":math:`\lambda \mathrm{=}0` ", "thermal conductivity"
    ":math:`\rho C\mathrm{=}2` ", "volume heat"



Boundary conditions and loads
-------------------------------------

Non-linear volume source loading, temperature dependent:

:math:`s(T)\mathrm{=}2\mathrm{-}2\mathrm{\times }w\mathrm{\times }T` with :math:`w\mathrm{=}2`

The boundary conditions are adiabatic, which corresponds to the defect in *Code_Aster*.

The time range :math:`\mathrm{[}0.;1.\mathrm{]}` is discretized into 100 time steps (duration of each time step equal to :math:`0.01`).


Initial conditions
--------------------

:math:`\mathit{T0}\mathrm{=}0` throughout the element.