A modified graded mesh and higher order finite element method for singularly perturbed reaction–diffusion problems

Aditya Kaushik, Vijayant Kumar, Manju Sharma and Nitika Sharma

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 185, issue C, 486-496

Abstract: This paper presents a modified graded mesh for singularly perturbed reaction–diffusion problems. The mesh we offer is generated recursively using Newton’s algorithm and some implicitly defined function. The problem is solved numerically using the finite element method based on polynomials of degree p≥1. We prove parameter uniform convergence of optimal order in ϵ-weighted energy norm. Test examples are taken, and we present a rigorous comparative analysis with other adaptive meshes. Moreover, we compare the proposed method with others found in the literature.

Keywords: Reaction–diffusion; Singular perturbation; Graded mesh; Finite element method (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:185:y:2021:i:c:p:486-496

DOI: 10.1016/j.matcom.2021.01.006

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