Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor and Francis Ltd.
Erişim Hakkı
info:eu-repo/semantics/embargoedAccess
Özet
A weak Galerkin finite element method is applied to singularly perturbed delay reaction-diffusion problems. A robust uniform convergence has been proved both in the energy and balanced norms using higher-order piecewise discontinuous polynomials on Shishkin meshes. The error analysis for singularly perturbed reaction-diffusion problems with negative or positive shift in the balanced norm has appeared for the first time. The proposed method uses piecewise polynomials of order (Formula presented.) on interior of each element and piecewise constant polynomials on the end points of each element. By the Schur complement technique, the interior degrees of foredoom (DOF) can be eliminated from the discrete system resulting from the numerical scheme, and thus the degrees of freedom of the proposed method comparable with the classical finite element methods, and it is remarkably less than that of the discontinuous Galerkin method. Finally, we give various numerical experiments to verify the theoretical findings.
Açıklama
Anahtar Kelimeler
Balanced Norm, Shishkin Meshes, Singularly Perturbed Differential-Difference Equation, Uniform Convergence, Weak Galerkin Finite Element Method
Kaynak
Journal of Difference Equations and Applications
WoS Q Değeri
Scopus Q Değeri
Q1
Cilt
30
Sayı
4
