Numerical analysis of a thermal problem arising in microstretch elastic plates

Abstract

In this work we study, from the numerical point of view, a thermoelastic problem involving a microstretch plate. The variational problem is written as a linear system composed of parabolic equations written in terms of the velocity field, the microrotations speed, the microstretch speed and the temperature. Then, a fully discrete approximation is introduced by using the finite element method and an Euler scheme. A priori error estimates are proved and the linear convergence of the algorithm is shown. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the solution.

Keywords:

• A priori estimates
• finite elements
• microstretch
• numerical simulations
• plates
• thermoelasticity

Additional information

Funding

The work of J. R. Fernández has been supported by the research project PGC2018-096696-B-I00 (Ministerio de Ciencia, Innovación y Universidades, Spain) with the participation of FEDER.