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Keywords:
electro-elasticity; bounded penalty; Signorini modified contact problem; nonlocal Coulomb's friction; Schauder's fixed point; regularized variational problem; error estimate; iterative method
electro-elasticity; bounded penalty; Signorini modified contact problem; nonlocal Coulomb's friction; Schauder's fixed point; regularized variational problem; error estimate; iterative method
Summary:
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 ${\epsilon }$, establishing a convergence rate of $O(\sqrt {\epsilon })$. Finally, we propose an iterative method to numerically solve the regularized problem and prove its convergence.
References:
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