Analysis of two thermoelastic problems with the Green–Lindsay model

Abstract In this paper, we analyze, from the numerical point of view, two thermo-elastic problems involving Green–Lindsay theory. The coupling term is different for each case, second order or first spatial derivatives, respectively. variational formulation leads to a linear coupled system which written in terms velocity and temperature speed. An existence uniqueness results exponential energy decay problem with stronger are recalled. polynomial weaker then proved but using theory semigroups. Then, fully discrete approximation introduced finite element method an implicit scheme. A stability property main priori error estimates result shown, can derive convergence approximations. Finally, some simulations presented demonstrate accuracy algorithm, dependence on relaxation parameter.