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Numerical analysis for a thermoelastic diffusion problem in moving boundary

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  • Madureira, Rodrigo L.R.
  • Rincon, Mauro A.
  • Aouadi, Moncef

Abstract

In the present study, a novel numerical method solving a thermoelastic diffusion problem with moving boundary is presented. Since the thermoelastic diffusion system is composed of three coupled differential equations, we propose an uncoupled numerical method to obtain an approximate numerical solution with quadratic convergence order in time and space. The error estimate in Sobolev space and order of convergence are obtained for the semi-discrete and fully discrete problem. The numerical approximation is based on the finite element method together with the Neumark’s approximation in time discretization. Finally, we will show that the results of the numerical simulation are in agreement with the numerical analysis.

Suggested Citation

  • Madureira, Rodrigo L.R. & Rincon, Mauro A. & Aouadi, Moncef, 2021. "Numerical analysis for a thermoelastic diffusion problem in moving boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 630-655.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:630-655
    DOI: 10.1016/j.matcom.2021.03.032
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    1. Madureira, Rodrigo L.R. & Rincon, Mauro A. & Aouadi, Moncef, 2019. "Global existence and numerical simulations for a thermoelastic diffusion problem in moving boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 410-431.
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    Cited by:

    1. Aatef D. Hobiny & Ibrahim A. Abbas, 2021. "Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model," Mathematics, MDPI, vol. 9(21), pages 1-11, November.
    2. Nepal, Surendra & Wondmagegne, Yosief & Muntean, Adrian, 2023. "Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants," Applied Mathematics and Computation, Elsevier, vol. 442(C).

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