Mathematical Analysis and Numerical Simulation of a Nonlinear Thermoelastic System. (26th October 2018)

• Record Type: Journal Article
• Authors: Carmo, B. A.; Clark, H. R.; Guardia, R. R.; Rincon, M. A.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 14(2018)
• Page Start: 1514
• Page End: 1542
• Publication Date: 2018-10-26
• Subjects: Convergence order -- energy behavior -- existence and uniqueness -- numerical simulations -- thermoelastic coupled system; 35L20 -- 34B15 -- 65M60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1486857
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: 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.