An exponential integrator-based discontinuous Galerkin method for linear complementarity systems

The linear complementarity system (LCS) is defined by a linear ordinary differential equation coupled with a finite-dimensional linear complementarity problem (LCP), which has many applications in engineering and economics. In this article, we reformulate the LCS with the boundary condition as an LCP in the Hilbert space of square-integrable functions, and propose a new numerical method for the LCS by using exponential Euler integrator and discontinuous Galerkin approximation. The precision of the proposed method is better than that of the existing time-stepping method in different magnitude of scale. Convergence analysis and numerical experiments are performed to support the arguments.