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A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator

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.

Keyword : ‎Sobolev space gradient method, WEB-spline finite element method, preconditioning operator, nonlinear parabolic problems

How to Cite
Salehi Shayegan, A. H., Zakeri, A., & Hosseini, S. M. (2020). A numerical method for solving two-dimensional nonlinear parabolic problems based on a preconditioning operator. Mathematical Modelling and Analysis, 25(4), 531-545. https://doi.org/10.3846/mma.2020.4310
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Oct 13, 2020
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