Reference solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

We have a simple analytical solution, since it involves exhibiting a harmonic function and adjusting the associated source in each domain:


* in field 1: :math:`T(x,y,z)=T({A}_{1})+{x}^{2}+{y}^{2}+{z}^{2}`, (in the original frame :math:`{A}_{1}`),


* in field 2: :math:`T(x,y,z)=T({A}_{2})+\frac{1}{2}{x}^{2}+{y}^{2}+{z}^{2}`, (in the original frame :math:`{A}_{2}`).

From this we deduce the values of :math:`{s}_{1}` and :math:`{s}_{2}`,, :math:`{s}_{1}=-6.`, :math:`{s}_{2}=–\mathrm{5.W}/{m}^{3}`.


Benchmark results
----------------------

Temperatures at the points on planes :math:`{B}_{1}{F}_{1}{G}_{1}{C}_{1}` and :math:`{A}_{2}{E}_{2}{H}_{2}{D}_{2}`


Uncertainty about the solution
---------------------------

Analytical solution.