Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations
| dc.contributor.author | Toprakseven, Şuayip | |
| dc.contributor.author | Tao, Xia | |
| dc.contributor.author | Hao, Jiaxiong | |
| dc.date.accessioned | 2024-12-02T12:16:02Z | |
| dc.date.available | 2024-12-02T12:16:02Z | |
| dc.date.issued | 2024 | |
| dc.department | AÇÜ, Artvin Meslek Yüksekokulu, Muhasebe ve Vergi Uygulamaları Bölümü | en_US |
| dc.description.abstract | 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. | |
| dc.identifier.doi | 10.1080/10236198.2023.2291154 | |
| dc.identifier.endpage | 464 | en_US |
| dc.identifier.issn | 1023-6198 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.scopusquality | Q1 | |
| dc.identifier.startpage | 435 | en_US |
| dc.identifier.uri | http://dx.doi.org/10.1080/10236198.2023.2291154 | |
| dc.identifier.uri | https://hdl.handle.net/11494/5086 | |
| dc.identifier.volume | 30 | en_US |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | en_US |
| dc.publisher | Taylor and Francis Ltd. | en_US |
| dc.relation.ispartof | Journal of Difference Equations and Applications | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/embargoedAccess | en_US |
| dc.subject | Balanced Norm | en_US |
| dc.subject | Shishkin Meshes | en_US |
| dc.subject | Singularly Perturbed Differential-Difference Equation | en_US |
| dc.subject | Uniform Convergence | en_US |
| dc.subject | Weak Galerkin Finite Element Method | en_US |
| dc.title | Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations | en_US |
| dc.type | Article |
