A new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem
This work provides a theoretical foundation for improved numerical methods for reaction-diffusion problems, but it is incremental as it only proposes a formulation without experimental validation or comparison to existing methods.
The paper introduces a new variational formulation for reaction-diffusion problems using a discontinuous Galerkin technique, proving its well-posedness and suggesting it will lead to hybrid numerical methods that are strongly stable in space, absolutely stable in time, and optimally convergent.
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.