Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection - diffusion - reaction problems
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Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This article focuses on constructing and analyzing a non-symmetric interior penalty Galerkin method (NIPG) on Shishkin mesh for solving singularly perturbed 2D elliptic boundary-value problems (BVPs). We use piecewise Lagrange interpolation at Gaussian points to improve the order of convergence of the interpolation error. We then study the superconvergence properties of the NIPG method and prove O(N-1 ln N)(k+1) order of convergence in the discrete energy-norm. Various numerical experiments are provided to validate the theoretical results.
Açıklama
Anahtar Kelimeler
Singularly perturbed 2D elliptic BVPs, convection-diffusion problem, Shishkin mesh, discontinuous Galerkin method with interior penalty, superconvergence
Kaynak
International Journal of Computer Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
100
Sayı
5
