Benchmark solution
=====================


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

The reference solution is the one recommended by Hughes and Brooks in their article cited as a bibliographical reference [:ref:`bib1 <bib1>`].

As an exact solution, we can take the temperature field from the upstream border projected onto the downstream border in the direction of the speed.


.. image:: images/10000000000005FD0000059BA5A788C64D8F8840.png
    :width: 2.5547in
    :height: 2.3917in


.. _RefImage_10000000000005FD0000059BA5A788C64D8F8840.png:


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

The temperatures are being tested on the border between points :math:`E` and :math:`D`.


.. image:: images/1000000000000CB3000002DCCAF076D03F367504.png
    :width: 5.4181in
    :height: 1.2201in


.. _RefImage_1000000000000CB3000002DCCAF076D03F367504.png:


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

Analytical solution.


Bibliographical references
---------------------------


* T.J.R. HUGHES, A. BROOKS "A multidimensional scheme with no crosswind diffusion" - T.J.R. HUGHES ed., Finite Element Methods for convection doninated flows, AMD Vol. 34 (ASME, New York (1979)).