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 ∈ 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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