Before revision:  We show that the new method which is obtained by using both continuous and discontinuous discretisations in space, admits  local and global conservation laws of energyand momentum. We show existence and uniqueness of solution of the discrete equations.
After revision:  We show that the new method which is obtained by using both continuous and discontinuous discretisations in space, admits local and global conservation law of energy. We also show existence and uniqueness of solution of the discrete equations.