A Uniformly Convergent Numerical Scheme for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations. (26th July 2020)

• Record Type: Journal Article
• Authors: Singh, Gautam; Natesan, Srinivasan
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 10(2020)
• Page Start: 1172
• Page End: 1189
• Publication Date: 2020-07-26
• Subjects: Discontinuous Galerkin finite element method -- Shishkin mesh -- singularly perturbed system of reaction-diffusion boundary-value problems -- uniform convergence; AMS 65L10 -- 65L11 -- 65L60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1740255
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Here, we study the numerical solution of singularly perturbed system of two-point boundary-value problems of reaction-diffusion type. The solutions of these problems exhibit twin overlapping exponential boundary layers. To obtain the numerical solutions of these problems, we apply the nonsymmetric discontinuous Galerkin FEM with interior penalties (NIPG method) on layer-adapted piecewise-uniform Shishkin mesh. Also, we have proved that the proposed method is uniformly convergent with order k in the ( ε, μ ) − weighted DG energy norm, where k is the degree of the piecewise polynomial in the finite element space. Numerical results are presented to support the theoretical results.