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A thermoelastic problem with diffusion, microtemperatures, and microconcentrations

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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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Authors and Affiliations

  1. Departamento de Matemática Aplicada I, Universidade de Vigo, ETSI Telecomunicación Campus As Lagoas Marcosende s/n, 36310, Vigo, Spain

    Noelia Bazarra & José R. Fernández

  2. Departamento de Matemáticas, ETS de Ingenieros de Caminos, Canales y Puertos Universidade da Coruña, Campus de Elviña, 15071, A Coruña, Spain

    Marco Campo

Authors
  1. Noelia Bazarra
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  2. Marco Campo
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  3. José R. Fernández
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Correspondence to José R. Fernández.

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This work has been supported by the Ministerio de Economía y Competitividad under the research project MTM2015-66640-P with FEDER Funds.

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Bazarra, N., Campo, M. & Fernández, J.R. A thermoelastic problem with diffusion, microtemperatures, and microconcentrations. Acta Mech 230, 31–48 (2019). https://doi.org/10.1007/s00707-018-2273-5

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  • DOI: https://doi.org/10.1007/s00707-018-2273-5

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