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<p>We consider the bounded penalty method to solve the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity studied in I. El Ouardy, Y. Mandyly, H. Benkhira, and R. Fakhar (2024). We formulate a regularized variational problem and prove the existence and uniqueness of its solution using elliptic quasi-variational inequalities, strongly monotone operators, and Schauder’s fixed point theorem. We also derive error estimates that depend on the penalty parameter ϵ, establishing a convergence rate of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(\sqrt{\epsilon})\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>O</mi> <mo stretchy="false">(</mo> <msqrt> <mi>ϵ</mi> </msqrt> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>. Finally, we propose an iterative method to numerically solve the regularized problem and prove its convergence.</p>

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Bounded penalty method for the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • El-Hassan Benkhira,
  • Ilham El Ouardy,
  • Youssef Mandyly,
  • Rachid Fakhar

摘要

We consider the bounded penalty method to solve the modified Signorini contact problem with nonlocal Coulomb’s friction in electro-elasticity studied in I. El Ouardy, Y. Mandyly, H. Benkhira, and R. Fakhar (2024). We formulate a regularized variational problem and prove the existence and uniqueness of its solution using elliptic quasi-variational inequalities, strongly monotone operators, and Schauder’s fixed point theorem. We also derive error estimates that depend on the penalty parameter ϵ, establishing a convergence rate of \(O(\sqrt{\epsilon})\) O ( ϵ ) . Finally, we propose an iterative method to numerically solve the regularized problem and prove its convergence.