2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The reference solution was obtained with the finite element calculation software « IVOHEAT » [bib2] cited in reference [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 \({10}^{-6}\).

2.2. Benchmark results#

Temperature at:

  • \(t=10s\) for \(x=0.01,0.02,0.04,0.06,0.08\) and \(0.1\),

  • \(t=13s\) for \(x=0.01,0.02,0.04,0.06,0.08\) and \(0.1\).

2.3. Bibliographical references#

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

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