Finite element method for the reconstruction of a time-dependent heat source in isotropic thermoelasticity systems of type-III

The isotropic thermoelasticity system of type-III, describing both the mechanical and thermal behaviours a body occupying bounded domain with Lipschitz boundary, is considered. displacement vector either normal heat flux or temperature are prescribed on boundary. Both theoretical numerical reconstructions time-dependent source from knowledge an additional weighted integral measurement investigated. It shown that appropriate type depends boundary condition available, whilst existence uniqueness weak solution for exact data also proved. For each two inverse problems investigated herein, algorithm proposed convergence these schemes Four examples noisy measurements implemented using finite element method thoroughly to validate stability algorithms.