Two-level finite element variational multiscale method based on bubble functions for the steady incompressible MHD flow. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Zhang, Tong; Qian, Yanxia; HuangFu, YuGao
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 3(2017)
• Page Start: 515
• Page End: 535
• Publication Date: 2017-03-04
• Subjects: Two-level method -- steady incompressible MHD -- variational multiscale method -- bubble function; 65M12; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2015.1115023
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, a finite element variational multiscale method (VMM) is developed for the stationary incompressible magnetohydrodynamics (MHD) problem and the corresponding stability and convergence are established. Our VMM is based on the polynomial bubble functions as a subgrid scale and the numerical implementation is based on the local Gauss integrations. Compared to the common VMM, our method does not introduce any extra variable. Furthermore, the two-level finite element VMM is also developed. Compared to the one-level VMM, the two-level VMM consists of solving a nonlinear MHD problem on a coarse mesh with mesh size H, and then a linearized magnetohydrodynamic problem based on the Oseen iteration on a fine mesh is solved with mesh sizeh ( h ≪ H ) . Stability and convergence of numerical approximations in two-level VMM are presented. Finally, some numerical examples are provided to demonstrate the effectiveness of the developed numerical algorithms.