A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator
This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on c...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2020-10-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/4310 |
| _version_ | 1818765345435942912 |
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| author | Amir Hossein Salehi Shayegan Ali Zakeri Seyed Mohammad Hosseini |
| author_facet | Amir Hossein Salehi Shayegan Ali Zakeri Seyed Mohammad Hosseini |
| author_sort | Amir Hossein Salehi Shayegan |
| collection | DOAJ |
| description | This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods. |
| first_indexed | 2024-12-18T08:16:37Z |
| format | Article |
| id | doaj.art-a0f6a482c63b437fb742e0b23be550e8 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T08:16:37Z |
| publishDate | 2020-10-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-a0f6a482c63b437fb742e0b23be550e82022-12-21T21:14:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102020-10-0125410.3846/mma.2020.4310A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operatorAmir Hossein Salehi Shayegan0Ali Zakeri1Seyed Mohammad Hosseini2K.N. Toosi University of Technology, Faculty of Mathematics, 16315–1618 Tehran, IranK.N. Toosi University of Technology, Faculty of Mathematics, 16315–1618 Tehran, IranTarbiat Modares University, Department of Applied Mathematics, 14115–175 Tehran, IranThis article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods.https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/4310Sobolev space gradient methodWEB-spline finite element methodpreconditioning operatornonlinear parabolic problems |
| spellingShingle | Amir Hossein Salehi Shayegan Ali Zakeri Seyed Mohammad Hosseini A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator Mathematical Modelling and Analysis Sobolev space gradient method WEB-spline finite element method preconditioning operator nonlinear parabolic problems |
| title | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
| title_full | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
| title_fullStr | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
| title_full_unstemmed | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
| title_short | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
| title_sort | numerical method for solving two dimensional nonlinear parabolic problems based on a preconditioning operator |
| topic | Sobolev space gradient method WEB-spline finite element method preconditioning operator nonlinear parabolic problems |
| url | https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/4310 |
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