Fully mixed finite element methods for thermoelastic contact
Abstract
We investigate the unique solvability of nonlinear static contact problems incorporating thermal effects and propose appropriate mixed finite element spaces for their numerical approximation. The fully mixed formulation simultaneously resolves the Cauchy stress, displacement, rotation tensor, temperature and heat flux, with nonlinearities arising from the bulk and contact thermomechanical coupling. The weak formulation is analysed within the framework of perturbed saddle-point problems in Banach spaces, employing fixed-point techniques alongside suitably defined variational inequalities. Error estimates are derived for general Galerkin discretisations, and convergence rates are established for Arnold-Falk-Winther elements for the mechanical variables, coupled with Brezzi-Douglas-Marini elements and piecewise polynomials for the thermal unknowns. Finally, several numerical experiments are presented, confirming the theoretical convergence results and demonstrating the robust performance of the proposed method.
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BibTeX
@misc{carrasco2026fully,
title = {{Fully mixed finite element methods for thermoelastic contact}},
author = {Sergio Carrasco and Franz Chouly and Alberto F Martin and Ricardo Ruiz Baier},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05625864v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fully mixed finite element methods for thermoelastic contact
AU - Sergio Carrasco
AU - Franz Chouly
AU - Alberto F Martin
AU - Ricardo Ruiz Baier
PY - 2026
DA - 2026/10/28
PB - HAL
UR - https://hal.science/hal-05625864v2
AB - We investigate the unique solvability of nonlinear static contact problems incorporating thermal effects and propose appropriate mixed finite element spaces for their numerical approximation. The fully mixed formulation simultaneously resolves the Cauchy stress, displacement, rotation tensor, temperature and heat flux, with nonlinearities arising from the bulk and contact thermomechanical coupling. The weak formulation is analysed within the framework of perturbed saddle-point problems in Banach spaces, employing fixed-point techniques alongside suitably defined variational inequalities. Error estimates are derived for general Galerkin discretisations, and convergence rates are established for Arnold-Falk-Winther elements for the mechanical variables, coupled with Brezzi-Douglas-Marini elements and piecewise polynomials for the thermal unknowns. Finally, several numerical experiments are presented, confirming the theoretical convergence results and demonstrating the robust performance of the proposed method.
ER -