  We put forward and analyze an explicit finite difference scheme for the
Camassa-Holm shallow water equation that can handle general $H^1$ initial data
and thus peakon-antipeakon interactions. Assuming a specified condition
restricting the time step in terms of the spatial discretization parameter, we
prove that the difference scheme converges strongly in $H^1$ towards a
dissipative weak solution of Camassa-Holm equation.
