A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes
In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtai...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-08-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024232 |
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| author | Suayip Toprakseven Seza Dinibutun |
| author_facet | Suayip Toprakseven Seza Dinibutun |
| author_sort | Suayip Toprakseven |
| collection | DOAJ |
| description | In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings. |
| format | Article |
| id | doaj-art-df74df44919f459384a8b66cd2c66e7e |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-df74df44919f459384a8b66cd2c66e7e2025-01-23T07:51:27ZengAIMS PressElectronic Research Archive2688-15942024-08-013285033506610.3934/era.2024232A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshesSuayip Toprakseven0Seza Dinibutun1Department of Mathematics, Yozgat Bozok University, Yozgat, TurkeyDepartment of Mathematics and Natural Sciences, International University of Kuwait, Ardiya, KuwaitIn this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.https://www.aimspress.com/article/doi/10.3934/era.2024232time dependent singularly perturbed problemweak galerkin methodsemi-discrete and fully discrete schemeslayer-adapted-meshes |
| spellingShingle | Suayip Toprakseven Seza Dinibutun A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes Electronic Research Archive time dependent singularly perturbed problem weak galerkin method semi-discrete and fully discrete schemes layer-adapted-meshes |
| title | A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes |
| title_full | A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes |
| title_fullStr | A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes |
| title_full_unstemmed | A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes |
| title_short | A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes |
| title_sort | weak galerkin finite element method for parabolic singularly perturbed convection diffusion equations on layer adapted meshes |
| topic | time dependent singularly perturbed problem weak galerkin method semi-discrete and fully discrete schemes layer-adapted-meshes |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024232 |
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