  In this paper, we study the Mach reflection phenomenon in inviscid flows
using a higher order discontinuous Galerkin method and overset grids. We use
the shock capturing procedure proposed in Siva Prasad Kochi et al. using
overset grids to capture the discontinuities occurring in the supersonic flow
over a wedge accurately. In this procedure, we obtain a coarse grid solution
first and using the troubled cell data, we construct an overset grid which is
approximately aligned to all the discontinuities. We rerun the solver with the
coarse grid solution as the initial condition while using the troubled cell
indicator and the limiter only on the overset grid. This allows us to capture
the discontinuities accurately. Using this procedure, we have obtained the
solution for Mach $3.0$ and $4.0$ flow over a wedge for various wedge angles
and determined the detachment criterion and the Von Neumann condition
accurately. We have also determined the Mach stem height for various wedge
angles for these Mach numbers. We have also demonstrated the hysteresis that
occurs in the transition from regular reflection to Mach reflection.
