Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation
| dc.contributor.author | Karasozen, Bulent | |
| dc.contributor.author | Uzunca, Murat | |
| dc.contributor.author | Sariaydin-Filibelioglu, Ayse | |
| dc.contributor.author | Yucel, Hamdullah | |
| dc.date.accessioned | 2025-05-10T17:04:41Z | |
| dc.date.available | 2025-05-10T17:04:41Z | |
| dc.date.issued | 2018 | |
| dc.description | Uzunca, Murat/0000-0001-5262-063X | en_US |
| dc.description.abstract | In this paper, we investigate numerical solution of Allen-Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF method as the time integrator for gradient systems like the Allen-Cahn equation satisfies the energy decreasing property for fully discrete scheme. Numerical results reveal that the discrete energy decreases monotonically, the phase separation and metastability phenomena can be observed, and the ripening time is detected correctly. | en_US |
| dc.description.sponsorship | Scientific HR Development Program (OYP) of the Turkish Higher Education Council (YOK) | en_US |
| dc.description.sponsorship | This work has been supported by Scientific HR Development Program (OYP) of the Turkish Higher Education Council (YOK). The authors would like to express their sincere thanks to the referees for the most valuable suggestions. | en_US |
| dc.identifier.doi | 10.1142/S0219876218500135 | |
| dc.identifier.issn | 0219-8762 | |
| dc.identifier.issn | 1793-6969 | |
| dc.identifier.scopus | 2-s2.0-85023175963 | |
| dc.identifier.uri | https://doi.org/10.1142/S0219876218500135 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14720/6092 | |
| dc.language.iso | en | en_US |
| dc.publisher | World Scientific Publ Co Pte Ltd | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Allen-Cahn Equation | en_US |
| dc.subject | Gradient Systems | en_US |
| dc.subject | Discontinuous Galerkin Method | en_US |
| dc.subject | Unconditional Energy Stability | en_US |
| dc.subject | Time Adaptivity | en_US |
| dc.title | Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.id | Uzunca, Murat/0000-0001-5262-063X | |
| gdc.author.scopusid | 6603369633 | |
| gdc.author.scopusid | 56175645700 | |
| gdc.author.scopusid | 57192154638 | |
| gdc.author.scopusid | 55762734500 | |
| gdc.author.wosid | Yucel, Hamdullah/J-5488-2017 | |
| gdc.author.wosid | Uzunca, Murat/P-1166-2018 | |
| gdc.coar.access | open access | |
| gdc.coar.type | text::journal::journal article | |
| gdc.description.department | T.C. Van Yüzüncü Yıl Üniversitesi | en_US |
| gdc.description.departmenttemp | [Karasozen, Bulent] Middle East Tech Univ, Dept Math, Ankara, Turkey; [Karasozen, Bulent; Sariaydin-Filibelioglu, Ayse; Yucel, Hamdullah] Middle East Tech Univ, Inst Appl Math, Ankara, Turkey; [Uzunca, Murat] Univ Turkish Aeronaut Assoc, Dept Ind Engn, Ankara, Turkey; [Sariaydin-Filibelioglu, Ayse] Yuzuncu Yil Univ, Econometry Dept, Van, Turkey | en_US |
| gdc.description.issue | 3 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q2 | |
| gdc.description.volume | 15 | en_US |
| gdc.description.woscitationindex | Science Citation Index Expanded | |
| gdc.description.wosquality | Q3 | |
| gdc.identifier.wos | WOS:000430848500005 | |
| gdc.index.type | WoS | |
| gdc.index.type | Scopus |