A P0–P0 weak Galerkin finite element method for solving singularly perturbed reaction–diffusion problems. Issue 2 (24th July 2019)

• Record Type: Journal Article
• Authors: Al‐Taweel, Ahmed; Hussain, Saqib; Wang, Xiaoshen; Jones, Brian
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 2(2020)
• Page Start: 213
• Page End: 227
• Publication Date: 2019-07-24
• Subjects: discrete gradient -- finite element methods -- reaction–diffusion system -- singular perturbation -- weak Galerkin; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22415
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: This paper investigates the lowest‐order weak Galerkin finite element (WGFE) method for solving reaction–diffusion equations with singular perturbations in two and three space dimensions. The system of linear equations for the new scheme is positive definite, and one might readily get the well‐posedness of the system. Our numerical experiments confirmed our error analysis that our WGFE method of the lowest order could deliver numerical approximations of the order O ( h 1/2 ) and O ( h ) in H 1 and L 2 norms, respectively.