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Volume 13, Issue 4
A Priori Error Estimates of a Signorini Contact Problem for Electro-Elastic Materials

S. Bourichi, El-H. Essoufi & R. Fakhar

Int. J. Numer. Anal. Mod., 13 (2016), pp. 627-647.

Published online: 2016-07

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  • Abstract

We consider a mathematical model for a static process of frictionless unilateral contact between a piezoelectric body and a conductive foundation. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution for the problem is established. We use the penalty method applied to the frictionless unilateral contact model to replace the Signorini contact condition, we show the existence of a unique solution, and derive error estimates. Moreover, under appropriate regularity assumptions of the solution, we have the convergence of the continuous penalty solution as the penalty parameter ϵ vanishes. Then, the numerical approximation of a penalty problem by using the finite element method is introduced. The error estimates are derived and convergence of the scheme is deduced under suitable regularity conditions.

  • Keywords

Piezoelectric, variational inequality, Signorini condition, penalty method, fixed point process, finite element approximation, error estimates.

  • AMS Subject Headings

35J85, 49J40, 74M10, 74M15, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-627, author = {S. Bourichi, El-H. Essoufi and R. Fakhar}, title = {A Priori Error Estimates of a Signorini Contact Problem for Electro-Elastic Materials}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {4}, pages = {627--647}, abstract = {

We consider a mathematical model for a static process of frictionless unilateral contact between a piezoelectric body and a conductive foundation. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution for the problem is established. We use the penalty method applied to the frictionless unilateral contact model to replace the Signorini contact condition, we show the existence of a unique solution, and derive error estimates. Moreover, under appropriate regularity assumptions of the solution, we have the convergence of the continuous penalty solution as the penalty parameter ϵ vanishes. Then, the numerical approximation of a penalty problem by using the finite element method is introduced. The error estimates are derived and convergence of the scheme is deduced under suitable regularity conditions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/456.html} }
TY - JOUR T1 - A Priori Error Estimates of a Signorini Contact Problem for Electro-Elastic Materials AU - S. Bourichi, El-H. Essoufi & R. Fakhar JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 627 EP - 647 PY - 2016 DA - 2016/07 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/456.html KW - Piezoelectric, variational inequality, Signorini condition, penalty method, fixed point process, finite element approximation, error estimates. AB -

We consider a mathematical model for a static process of frictionless unilateral contact between a piezoelectric body and a conductive foundation. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution for the problem is established. We use the penalty method applied to the frictionless unilateral contact model to replace the Signorini contact condition, we show the existence of a unique solution, and derive error estimates. Moreover, under appropriate regularity assumptions of the solution, we have the convergence of the continuous penalty solution as the penalty parameter ϵ vanishes. Then, the numerical approximation of a penalty problem by using the finite element method is introduced. The error estimates are derived and convergence of the scheme is deduced under suitable regularity conditions.

S. Bourichi, El-H. Essoufi and R. Fakhar. (2016). A Priori Error Estimates of a Signorini Contact Problem for Electro-Elastic Materials. International Journal of Numerical Analysis and Modeling. 13 (4). 627-647. doi:
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