High Order Hierarchical Divergence-Free Constrained Transport $H(div)$ Finite Element Method for Magnetic Induction Equation
Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 2 : pp. 243–254
Abstract
In this paper, we propose to use the interior functions of an hierarchical basis for high order $BDM_p$ elements to enforce the divergence-free condition of a magnetic field $B$ approximated by the $H(div)$ $BDM_p$ basis. The resulting constrained finite element method can be used to solve magnetic induction equation in MHD equations. The proposed procedure is based on the fact that the scalar ($p-1$)-th order polynomial space on each element can be decomposed as an orthogonal sum of the subspace defined by the divergence of the interior functions of the $p$-th order $BDM_p$ basis and the constant function. Therefore, the interior functions can be used to remove element-wise all higher order terms except the constant in the divergence error of the finite element solution of the $B$-field. The constant terms from each element can be then easily corrected using a first order $H(div)$ basis globally. Numerical results for a 3-D magnetic induction equation show the effectiveness of the proposed method in enforcing divergence-free condition of the magnetic field.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.s03
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 2 : pp. 243–254
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
-
Finite element iterative algorithm based on Anderson acceleration technique for incompressible MHD equations
Dong, Xiaojing | Huang, Yunqing | Liu, Meiyun | Tang, QiliJournal of Computational and Applied Mathematics, Vol. 448 (2024), Iss. P.115930
https://doi.org/10.1016/j.cam.2024.115930 [Citations: 0] -
Local and parallel finite element algorithm based on the partition of unity method for the incompressible MHD flow
Dong, Xiaojing | He, Yinnian | Wei, Hongbo | Zhang, YuhongAdvances in Computational Mathematics, Vol. 44 (2018), Iss. 4 P.1295
https://doi.org/10.1007/s10444-017-9582-4 [Citations: 19] -
A Global Divergence Conforming DG Method for Hyperbolic Conservation Laws with Divergence Constraint
Chandrashekar, Praveen
Journal of Scientific Computing, Vol. 79 (2019), Iss. 1 P.79
https://doi.org/10.1007/s10915-018-0841-4 [Citations: 4] -
Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem
Zeng, Yuping | Weng, Zhifeng | Liang, FenDiscrete Dynamics in Nature and Society, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/9464389 [Citations: 1]