A high-order stabilizer-free weak Galerkin finite element method on nonuniform time meshes for subdiffusion problems
| dc.contributor.author | Toprakseven, Şuayip | |
| dc.contributor.author | Dinibütün, Seza | |
| dc.date.accessioned | 2025-07-25T08:34:46Z | |
| dc.date.available | 2025-07-25T08:34:46Z | |
| dc.date.issued | 2023 | |
| dc.department | AÇÜ, Artvin Meslek Yüksekokulu, Muhasebe ve Vergi Uygulamaları Bölümü | |
| dc.description.abstract | We present a stabilizer-free weak Galerkin finite element method (SFWG-FEM) with polynomial reduction on a quasi-uniform mesh in space and Alikhanov’s higher order L2-1σ scheme for discretization of the Caputo fractional derivative in time on suitable graded meshes for solving time-fractional subdiffusion equations. Typical solutions of such problems have a singularity at the starting point since the integer-order temporal derivatives of the solution blow up at the initial point. Optimal error bounds in H1 norm and L2 norm are proven for the semi-discrete numerical scheme. Furthermore, we have obtained the values of user-chosen mesh grading constant r, which gives the optimal convergence rate in time for the fully discrete scheme. The optimal rate of convergence of order O(hk+1 + M−2) in the L∞ (L2)-norm has been established. We give several numerical examples to confirm the theory presented in this work. | |
| dc.identifier.doi | 10.3934/math.20231588 | |
| dc.identifier.endpage | 31049 | |
| dc.identifier.issn | 24736988 | |
| dc.identifier.issue | 12 | |
| dc.identifier.scopus | 2-s2.0-85177218299 | |
| dc.identifier.scopusquality | Q1 | |
| dc.identifier.startpage | 31022 | |
| dc.identifier.uri | https://hdl.handle.net/11494/5870 | |
| dc.identifier.volume | 8 | |
| dc.indekslendigikaynak | Scopus | |
| dc.institutionauthor | Toprakseven, Şuayip | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.relation.ispartof | AIMS Mathematics | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.subject | Graded temporal meshes | |
| dc.subject | Optimal rate of convergence | |
| dc.subject | Stabilizer-free weak Galerkin finite element method | |
| dc.subject | Sub-diffusion problems | |
| dc.title | A high-order stabilizer-free weak Galerkin finite element method on nonuniform time meshes for subdiffusion problems | |
| dc.type | Article |
