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<p>In this work, a particular class of penalized Signorini’s models with a normal compliance contact condition is studied. These contact models are created by taking two parameters: a power parameter <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>≥</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\alpha \geq 1$</EquationSource> </InlineEquation> and a punishment parameter <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> <EquationSource Format="TEX">$\varepsilon $</EquationSource> </InlineEquation>. A standard penalization is represented by a value of <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$\alpha =1$</EquationSource> </InlineEquation>. These contact models function as nonlinear approximations for Signorini’s problem. Choosing a continuous, conforming linear finite element approximation is the first step in our method. We then calculate <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation>-error estimates with suitable assumptions, which are carefully examined and explained.</p>

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Error Analysis of a Frictional Piezoelectric Contact Problem

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • H. El Khalfi,
  • Z. Faiz,
  • A. Oultou,
  • H. Benaissa

摘要

In this work, a particular class of penalized Signorini’s models with a normal compliance contact condition is studied. These contact models are created by taking two parameters: a power parameter α ≥ 1 $\alpha \geq 1$ and a punishment parameter ε $\varepsilon $ . A standard penalization is represented by a value of α = 1 $\alpha =1$ . These contact models function as nonlinear approximations for Signorini’s problem. Choosing a continuous, conforming linear finite element approximation is the first step in our method. We then calculate L 2 $L^{2}$ -error estimates with suitable assumptions, which are carefully examined and explained.