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


Reference quantities
----------------------

The solution is deduced from the following publication (chapter 4, "Numerical examples"):

Solidification problems by the boundary element method. Nicholas ZABARAS and S MUKHERJEE. Int Journal of Solids Structures. Pergamon. Vol. 31, No. 12/13, pp. 1829-1846, 1994


Benchmark result
---------------------


.. csv-table::

    ":math:`t(s)` ", "Points", "Size
    :math:`(°C)` ", "Reference"
    "1"," :math:`F` "," :math:`\mathrm{TEMP}` ", "-11.8"
    "2"," :math:`F` "," :math:`\mathrm{TEMP}` ", "-29.9"
    "3"," :math:`F` "," :math:`\mathrm{TEMP}` ", "-34.7"
    "4"," :math:`F` "," :math:`\mathrm{TEMP}` ", "-36.7"
    "", "", "", ""
    "1"," :math:`E` "," :math:`\mathrm{TEMP}` ", "0"
    "2"," :math:`E` "," :math:`\mathrm{TEMP}` ", "-18.1"
    "3"," :math:`E` "," :math:`\mathrm{TEMP}` ", "-25.2"
    "4"," :math:`E` "," :math:`\mathrm{TEMP}` ", "-29.3"







*