A modified weak galerkin finite element method for singularly perturbed parabolic convection-diffusion-reaction problems
Yükleniyor...
Dosyalar
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Global Science Press
Erişim Hakkı
info:eu-repo/semantics/embargoedAccess
Özet
In this work, a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion equations. The key feature of the proposed method is to replace the classical gradient and divergence operators by the modified weak gradient and modified divergence operators, respectively. We apply the backward finite difference method in time and the modified weak Galerkin finite element method in space on uniform mesh. The stability analyses are presented for both semi-discrete and fully-discrete modified weak Galerkin finite element methods. Optimal order of convergences are obtained in suitable norms. We have achieved the same accuracy with the weak Galerkin method while the degrees of freedom are reduced in our method. Various numerical examples are presented to support the theoretical results. It is theoretically and numerically shown that the method is quite stable.
Açıklama
Anahtar Kelimeler
Backward Euler method, Error estimates, Parabolic convection-diffusion problems, The modified weak Galerkin finite element method
Kaynak
Journal of Computational Mathematics
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
41
Sayı
6
