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Journal of Scientific Computing

Erschienen in:

01.05.2015

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

verfasst von: Xiaojing Dong, Yinnian He

Erschienen in: Journal of Scientific Computing | Ausgabe 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.

Vorheriger Artikel The Enriched Crouzeix–Raviart Elements are Equivalent to the Raviart–Thomas Elements

Nächster Artikel Local Analysis of Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem

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Titel: Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics
verfasst von: Xiaojing Dong
Yinnian He
Publikationsdatum: 01.05.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9900-7

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