A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator
DOI: https://doi.org/10.3846/mma.2020.4310Abstract
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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Sobolev space gradient method, WEB-spline finite element method, preconditioning operator, nonlinear parabolic problemsHow to Cite
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Copyright (c) 2020 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Copyright (c) 2020 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.