  An efficient time-stepping algorithm is proposed based on operator-splitting
and the space-time discontinuous Galerkin finite element method for problems in
the non-classical theory of thermoelasticity. The non-classical theory
incorporates three models; the classical theory based on Fourier's law of heat
conduction resulting in a hyperbolic-parabolic coupled system, a non-classical
theory of a fully hyperbolic extension, and a combination of the two. The
general problem is split into two contractive sub-problems, namely the
mechanical phase and the thermal phase. Each sub-problem is discretised using
space-time discontinuous Galerkin finite element method resulting each to be
stable which then leads to unconditional stability of the global product
algorithm. A number of numerical examples are presented to demonstrate the
performance and capability of the method.
