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Acta Mechanica

, Volume 230, Issue 1, pp 31–48 | Cite as

A thermoelastic problem with diffusion, microtemperatures, and microconcentrations

  • Noelia Bazarra
  • Marco Campo
  • José R. FernándezEmail author
Original Paper
  • 21 Downloads

Abstract

In this paper, we analyze, from the numerical point of view, a dynamic problem involving a thermoelastic body with diffusion, whose microelements are assumed to possess microtemperatures and microconcentrations. Using the linear theory, the mechanical problem is written as a coupled system of hyperbolic and parabolic partial differential equations for the displacement, temperature, chemical potential, microconcentrations, and microtemperatures fields. The variational formulation is derived, and it leads to a coupled system of parabolic linear variational equations, for which an existence and uniqueness result is stated. Then, using the finite element method and the implicit Euler scheme, fully discrete approximations are introduced. Stability properties and a priori error estimates are obtained, from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the accuracy of the approximation and the behaviour of the solution.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada IUniversidade de VigoVigoSpain
  2. 2.Departamento de MatemáticasETS de Ingenieros de Caminos, Canales y Puertos Universidade da CoruñaA CoruñaSpain

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