Finite element approximation of reaction–diffusion problems using an exponentially graded mesh. (15th November 2018)

• Record Type: Journal Article
• Authors: Constantinou, P.; Franz, S.; Ludwig, L.; Xenophontos, C.
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 10(2018)
• Page Start: 2523
• Page End: 2534
• Publication Date: 2018-11-15
• Subjects: Boundary layers -- Reaction–diffusion -- Exponential mesh -- Uniform optimal convergence -- Balanced norm; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.08.051
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present the analysis of an h version Finite Element Method for the approximation of the solution to singularly perturbed reaction–diffusion problems posed in smooth domains Ω ⊂ R 2 . The method uses piecewise polynomials of degree p in each variable, defined on an exponentially graded mesh, optimally constructed for the approximation of exponential layers. We establish robust, optimal convergence rates in a variety of norms and illustrate our theoretical findings through numerical computations.