Numerical Analysis of Hemivariational Inequalities
Inequality problems in mechanics can be divided into two main categories: that of variational inequalities concerned with convex energy functionals (potentials), and that of hemivariational inequalities concerned with nonsmooth and nonconvex energy functionals (superpotentials). Through the formulation of hemivariational inequalities, problems involving nonmonotone, nonsmooth and multivalued constitutive laws, forces, and boundary conditions can be treated successfully. Hemivariational inequalities have been shown to be very useful across a wide variety of subjects, ranging from nonsmooth mechanics, physics, engineering, to economics. This talk starts with a discussion of weak formulations of a model elliptic boundary value problems, followed by an introduction of variational inequalities and then that of hemivariational inequalities arising in contact mechanics. We present recent and new results on convergence and optimal order error estimates for numerical solutions of hemivariational inequalities. Numerical examples are shown on the performance of the numerical methods, including numerical convergence orders.