Accepted publication: An unconditionally stable algorithm for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods

An article co-authored by Dr Andrew McBride, Mebratu Fenta & Daya Reddy has been published in Computer Methods in Applied Mechanics and Engineering.

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 discretized using the space-time dis- continuous Galerkin finite element method. The sub-problems are 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. 

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