Convergence of regularized time-stepping methods for differential variational inequalities (Q2866201)

The authors consider differential equations with additional constraints represented by a variational inequality, which thus determines relations between two groups of variables. Unlike the previous versions of the time-stepping (finite difference) method, they utilize the Tikhonov regularization. Since the feasible set of the variational inequality is a Cartesian product, certain order monotonicity properties provide existence and uniqueness of each particular solution. The authors give some error bounds and establish convergence of approximate solutions to a weak solution of the initial problem. The results are specialized to the case where the variational inequality reduces to a linear complementarity problem. Some computational illustration of performance is also given.