Mathematical and numerical analysis of an obstacle problem for elastic piezoelectric beams

Abstract

[Abstract] We consider a mathematical model that describes the equilibrium of an electro-elastic beam in contact with an electrically conductive foundation (an obstacle). The model is constructed by coupling the beam equation with a system of equations describing one-dimensional piezoelectricity. We state the unique weak solvability of the model as well as the continuous dependence of the weak solution with respect to the data. We also introduce a discrete scheme for which we perform numerical analysis, including convergence and error estimate results. Finally, we present numerical simulations in the study of a test problem.