Mathematical Analysis and Numerical Simulation of a Nonlinear Thermoelastic System

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonl...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2018-10, Vol.39 (14), p.1514-1542
Main Authors: Carmo, B. A., Clark, H. R., Guardia, R. R., Rincon, M. A.
Format: Article
Language:English
Subjects:
Boundary conditions
Computer simulation
Convergence order
Decay rate
energy behavior
existence and uniqueness
Finite difference method
Finite element method
Mathematical models
Newton methods
Nonlinear systems
Numerical analysis
Numerical methods
numerical simulations
Thermodynamics
thermoelastic coupled system
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Summary:In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear non-local thermoelastic coupled system with linear boundary conditions. Furthermore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time which results in a nonlinear system to be solved by Newton's method. Numerical experiments for one-dimensional and two-dimensional cases are presented in order to estimate the rate of convergence of the numerical solution that confirm our analysis and show the efficiency of the method.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1486857