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

Calculation method used for the reference solution
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The reference solution was obtained with the finite element calculation software "IVOHEAT" [:ref:`bib2 <bib2>`] cited in reference [:ref:`bib1 <bib1>`]. This solution is based on a mesh consisting of 20 isoparametric elements with 4 nodes of identical size, using a Crank-Nicolson method modified with a precision of :math:`{10}^{-6}`.


Benchmark results
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Temperature at:


* :math:`t=10s` for :math:`x=0.01,0.02,0.04,0.06,0.08` and :math:`0.1`,


* :math:`t=13s` for :math:`x=0.01,0.02,0.04,0.06,0.08` and :math:`0.1`.


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


* S. Orivuori, "Efficient method for solution of nonlinear heat conduction problems", Int. J. num. Meth. Engng, vol. 14, no. 10, pp. 1461-1476, 1979


* S. Orivuori, "A finite element method applied to the solution of the transient heat conduction problem", Licentiate Thesis, Tech. Univ., Helsinki (1977), in Finnish.