A new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem

TL;DR

This paper introduces a novel variational formulation using a unique discontinuous Galerkin approach for reaction-diffusion problems, aiming to improve stability and convergence of numerical solutions.

Contribution

It presents a new discontinuous Galerkin-based variational formulation that differs from existing methods, with proven well-posedness and potential for enhanced hybrid numerical schemes.

Findings

The new formulation is well-posed.

It is strongly stable in spatial variables.

It is absolutely stable in temporal variables.

Abstract

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.