Discontinuous Discretization for Least-Squares Formulation of Singularly Perturbed Reaction-Diffusion Problems in One and Two Dimensions

@article{Lin2008DiscontinuousDF,
  title={Discontinuous Discretization for Least-Squares Formulation of Singularly Perturbed Reaction-Diffusion Problems in One and Two Dimensions},
  author={Runchang Lin},
  journal={SIAM J. Numerical Analysis},
  year={2008},
  volume={47},
  pages={89-108}
}
In this paper, we consider the singularly perturbed reaction-diffusion problem in one and two dimensions. The boundary value problem is decomposed into a first-order system to which a suitable weighted least-squares formulation is proposed. A robust, stable, and efficient approach is developed based on local discontinuous Galerkin (LDG) discretization for the weak form. Uniform error estimates are derived. Numerical examples are presented to illustrate the method and the theoretical results… CONTINUE READING