Numerical analysis of a frictional contact problem for thermo-electro-elastic materials

A numerical method is presented for a mathematical model which describes the frictional contact between a thermo-electro-elastic body and a conductive foundation. The contact is described by Signorini’s conditions and Tresca’s friction law including electrical and ther- mal conductivity conditions. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme based on the finite element method. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.

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