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

TL;DR

This paper introduces an unconditionally stable, operator-splitting, space-time discontinuous Galerkin finite element algorithm for solving various models in non-classical thermoelasticity, ensuring stability and efficiency.

Contribution

The paper develops a novel, unconditionally stable algorithm combining operator-splitting and space-time DG methods for generalised thermoelasticity models.

Findings

The method is unconditionally stable for all models tested.

Numerical examples demonstrate high accuracy and stability.

The approach efficiently handles coupled hyperbolic-parabolic systems.

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.