A Numerical Method for SolvingTwo-Dimensional Nonlinear Parabolic ProblemsBased 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 co...

Full description

Saved in:
Bibliographic Details
Published inMathematical modelling and analysis Vol. 25; no. 4; pp. 531 - 545
Main Authors Salehi Shayegan, Amir Hossein, Zakeri, Ali, Hosseini, Seyed Mohammad
Format Journal Article
LanguageEnglish
Published 13.10.2020
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.4310