Tuning of the equilibrated residual method for applications in general, direct and inverse piezoelectricity

This paper presents application and tuning of the equilibrated residual method (ERM) of a posteriori error estimation for coupled electromechanical problems of direct, inverse and general piezoelectricity. In these three cases, either electric potential is induced by strains or strains appear due to the applied electric potential or both phenomena occur simultaneously. The mentioned ERM is assigned for the assessment of modeling and approximation errors of the numerical finite element solution. Such error values usually serve as indication for adaptive hierarchical modeling and adaptive mesh changes within thin and/or solid piezoelectric members so as to obtain the solution of assumed accuracy.