Numerical analysis of a piezoelectric contact problem with locking material and thermal effects

This paper investigates a new mathematical model of static frictional contact for an ideally locking piezoelectric material with electrical and thermal conductivity conditions. A variational formulation the is derived, in form coupled system displacements, electric potential temperature. The existence unique weak solution established its proof based on Tychonoff fixed point theorem multivalued operator. Moreover, discrete scheme finite element method introduced. Under some regularity assumptions, optimal order error estimates are derived.