Piecewise Integration of Differential Variational Inequality

Abstract

Differential variational inequality (DVI) is a new mathematical paradigm consisting of a system of ordinary differential equations and a parametric variational inequality problem as the constraints. The solution of DVI was shown at best piecewise differentiable, for which the existing integrators possess only convergence of order one. In this paper we present an algorithm of finding the pieces where the solution is differentiable, and propose applying the methods in the pieces for a moderate stepsize, while for smaller stepsize around the boundary of the pieces for achieving high accuracy. Numerical example of bridge collapse is given to illustrate the efficiency of our algorithms.