A parameter-uniform weak Galerkin finite element method for a coupled system of singularly perturbed reaction-diffusion equations
Yükleniyor...
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Faculty of Sciences and Mathematics, University of Nis, Serbia
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The aim of this paper to investigate a weak Galerkin finite element method (WG-FEM) for solving a system of coupled singularly perturbed reaction-diffusion equations. Each equation in the system has perturbation parameter of different magnitude and thus, the solutions will exhibit two distinct but overlapping boundary layers near each boundary of the domain. The proposed method is applied to the coupled system on Shishkin mesh to solve the problem theoretically and numerically. Elimination of the interior unknowns efficiently from the discrete solution system reduces the degrees of freedom and, thus the number of unknown in the discrete solution is comparable with the standard finite element scheme. The stability and error analysis of the proposed method on the Shishkin mesh are presented. We show that the method convergences of order O(N?k lnk N) in the energy norm, uniformly with respect to the perturbation parameter. Moreover, the optimal convergence rate of O(N?(k+1)) in the L 2 -norm and the superconvergence rate of O((N?2k ln2k N) in the discrete L ?-norm is observed numerically. Finally, some numerical experiments are carried out to verify numerically theory.
Açıklama
Anahtar Kelimeler
Kaynak
Filomat
WoS Q Değeri
Q2
Scopus Q Değeri
Cilt
37
Sayı
13
Künye
Toprakseven, Ş., & Zhu, P. (2023). A parameter-uniform weak Galerkin finite element method for a coupled system of singularly perturbed reaction-diffusion equations. Filomat. 37(13), 4351-4374.
