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An efficient time-stepping algorithm is proposed based on operator-splittingand the space-time discontinuous Galerkin finite element method for problems inthe non-classical theory of thermoelasticity. The non-classical theoryincorporates three models; the classical theory based on Fourier's law of heatconduction resulting in a hyperbolic-parabolic coupled system, a non-classicaltheory of a fully hyperbolic extension, and a combination of the two. Thegeneral problem is split into two contractive sub-problems, namely themechanical phase and the thermal phase. Each sub-problem is discretised usingspace-time discontinuous Galerkin finite element method resulting each to bestable which then leads to unconditional stability of the global productalgorithm. A number of numerical examples are presented to demonstrate theperformance and capability of the method.

An unconditionally stable algorithm for generalised thermoelasticity  based on operator-splitting and time-discontinuous Galerkin finite element  methods