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On the issue that Finite Element discretizations violate, nodally, Clausius’s postulate of the second law of thermodynamics

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Figure

Fig. 1 Piecewise linear element in 1D
Fig. 2 1D mesh discretization of space
Fig. 3 Time-evolution of nodal temperatures in a 1D-body using a consistent FE discretization with a meshof 4 nodes
Fig. 4 Zoom-in from Fig. 3 with time-evolution of nodal temperature T4(t)
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