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arXiv · 1505.00708

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

Mebratu F. Wakeni·B. D. Reddy·A. T. McBride
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Abstract

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.

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Mebratu F. Wakeni, B. D. Reddy, A. T. McBride. 2015-05-04. An unconditionally stable algorithm for generalised thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods. https://arxiv.org/abs/1505.00708

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