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...
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| Published in | Mathematical modelling and analysis Vol. 25; no. 4; pp. 531 - 545 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Vilnius
Vilnius Gediminas Technical University
13.10.2020
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| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. 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. Keywords: Sobolev space gradient method, WEB-spline finite element method, preconditioning operator, nonlinear parabolic problems. AMS Subject Classification: 35K55. |
| Audience | Academic |
| Author | Zakeri, Ali Salehi Shayegan, Amir Hossein Hosseini, Seyed Mohammad |
| Author_xml | – sequence: 1 givenname: Amir Hossein orcidid: 0000-0002-6077-5321 surname: Salehi Shayegan fullname: Salehi Shayegan, Amir Hossein organization: K.N. Toosi University of Technology, Faculty of Mathematics, 16315–1618 Tehran, Iran – sequence: 2 givenname: Ali orcidid: 0000-0002-6273-7855 surname: Zakeri fullname: Zakeri, Ali organization: K.N. Toosi University of Technology, Faculty of Mathematics, 16315–1618 Tehran, Iran – sequence: 3 givenname: Seyed Mohammad surname: Hosseini fullname: Hosseini, Seyed Mohammad organization: Tarbiat Modares University, Department of Applied Mathematics, 14115–175 Tehran, Iran |
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| Copyright | Copyright (c) 2020 The Author(s). Published by Vilnius Gediminas Technical University. COPYRIGHT 2020 Vilnius Gediminas Technical University 2020. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| SubjectTerms | Approximation Boundary value problems Error analysis Finite element analysis Finite element method Ill-conditioned problems (mathematics) Iterative methods Mathematical analysis Mathematical research Meshless methods Methods nonlinear parabolic problems Nonlinear systems Nonlinear theories Numerical analysis Numerical methods Preconditioning preconditioning operator Sobolev space Sobolev space gradient method Sobolev spaces WEB-spline finite element method |
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| Title | A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator |
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