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Published in: Journal of Scientific Computing 2/2015

01-05-2015

Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics

Authors: Xiaojing Dong, Yinnian He

Published in: Journal of Scientific Computing | Issue 2/2015

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Abstract

In this paper, Newton iteration and two-level finite element algorithm are combined for solving numerically the stationary incompressible magnetohydrodynamics (MHD) under a strong uniqueness condition. The method consists of solving the nonlinear MHD system by \(m\) Newton iterations on a coarse mesh with size \(H\) and then computing the Stokes and Maxwell problems on a fine mesh with size \(h\ll H\). The uniform stability and optimal error estimates of both Newton iterative method and two-level Newton iterative method are given. The error analysis shows that the two-level Newton iterative solution is of the same convergence order as the Newton iterative solution on a fine grid with \(h=O(H^2)\). However, the two-level Newton iterative method for solving the stationary incompressible MHD equations is simpler and more efficient than Newton iterative one. Finally, the effectiveness of the two-level Newton iterative method is illustrated by several numerical investigations.

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Metadata
Title
Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics
Authors
Xiaojing Dong
Yinnian He
Publication date
01-05-2015
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-014-9900-7

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