Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems

Mustapha Bouallala

Applications of Mathematics (2024)

  • Volume: 69, Issue: 4, page 451-479
  • ISSN: 0862-7940

Abstract

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We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here's a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation.

How to cite

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Bouallala, Mustapha. "Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems." Applications of Mathematics 69.4 (2024): 451-479. <http://eudml.org/doc/299538>.

@article{Bouallala2024,
abstract = {We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here's a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation.},
author = {Bouallala, Mustapha},
journal = {Applications of Mathematics},
keywords = {hemivariational inequality; Rothe method; Clarke subdifferential; Caputo derivative; fractional viscoelastic constitutive law; contact with friction; numerical scheme; finite element method; convergence analysis; error estimation},
language = {eng},
number = {4},
pages = {451-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems},
url = {http://eudml.org/doc/299538},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Bouallala, Mustapha
TI - Weak solvability and numerical analysis of a class of time-fractional hemivariational inequalities with application to frictional contact problems
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 451
EP - 479
AB - We investigate a generalized class of fractional hemivariational inequalities involving the time-fractional aspect. The existence result is established by employing the Rothe method in conjunction with the surjectivity of multivalued pseudomonotone operators and the properties of the Clarke generalized gradient. We are also exploring a numerical approach to address the problem, utilizing both spatially semi-discrete and fully discrete finite elements, along with a discrete approximation of the fractional derivative. All these results are applied to the analysis and numerical approximations of a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The constitutive relation is modeled using the fractional Kelvin-Voigt law. The contact and friction are described by the subdifferential boundary conditions. The variational formulation of this problem leads to a fractional hemivariational inequality. The error estimates for this problem are derived. Finally, here's a second concrete example to illustrate the application. We propose a frictional contact model that incorporates normal compliance and Coulomb friction to describe the quasi-static contact between a viscoelastic body and a solid foundation.
LA - eng
KW - hemivariational inequality; Rothe method; Clarke subdifferential; Caputo derivative; fractional viscoelastic constitutive law; contact with friction; numerical scheme; finite element method; convergence analysis; error estimation
UR - http://eudml.org/doc/299538
ER -

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