  In this paper, a new variational formulation based on discontinuous Galerkin
technique for a reaction-diffusion problem is introduced, and the discontinuous
Galerkin technique of this work is different from the general discontinuous
Galerkin methods. The well posedness of the new formulation is given. Finally,
it is pointed that the new variational formulation will be helpful to design
better hybrid numerical methods which will not only strongly stable in spatial
variable and absolutely stable in temporal variable but also be optimally
convergent.
