Discontinuous discretization for least-squares formulation of singularly perturbed reaction-diffusion problems in one and two dimensions
SIAM Journal on Numerical Analysis
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 baaed 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. Comparison studies are made between the proposed method and other methods. © 2008 Society for Industrial and Applied Mathematics.
Lin, Runchang, "Discontinuous discretization for least-squares formulation of singularly perturbed reaction-diffusion problems in one and two dimensions" (2008). Mathematics & Physics Faculty Publications. 31.