Volume 30, Issue 6
A Discontinuous Galerkin Method for the Fourth-Order Curl Problem

Qingguo Hong, Jun Hu, Shi Shu & Jinchao Xu

J. Comp. Math., 30 (2012), pp. 565-578

Published online: 2012-12

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  • Abstract

In this paper, we present a discontinuous Galerkin (DG) method based on the N\'{e}d\'{e}lec finite element space for solving a fourth-order curl equation arising from a magnetohydrodynamics model on a 3-dimensional bounded Lipschitz polyhedron. We show that the method has an optimal error estimate for a model problem involving a fourth-order curl operator. Furthermore, some numerical results in 2 dimensions are presented to verify the theoretical results.

  • Keywords

Fourth-order curl problem DG method N\'{e}d\'{e}lec finite element space Error estimate

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-565, author = {Qingguo Hong, Jun Hu, Shi Shu and Jinchao Xu}, title = {A Discontinuous Galerkin Method for the Fourth-Order Curl Problem}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {6}, pages = {565--578}, abstract = { In this paper, we present a discontinuous Galerkin (DG) method based on the N\'{e}d\'{e}lec finite element space for solving a fourth-order curl equation arising from a magnetohydrodynamics model on a 3-dimensional bounded Lipschitz polyhedron. We show that the method has an optimal error estimate for a model problem involving a fourth-order curl operator. Furthermore, some numerical results in 2 dimensions are presented to verify the theoretical results. }, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1206-m3572}, url = {http://global-sci.org/intro/article_detail/jcm/8452.html} }
TY - JOUR T1 - A Discontinuous Galerkin Method for the Fourth-Order Curl Problem AU - Qingguo Hong, Jun Hu, Shi Shu & Jinchao Xu JO - Journal of Computational Mathematics VL - 6 SP - 565 EP - 578 PY - 2012 DA - 2012/12 SN - 30 DO - http://doi.org/10.4208/jcm.1206-m3572 UR - https://global-sci.org/intro/article_detail/jcm/8452.html KW - Fourth-order curl problem KW - DG method KW - N\'{e}d\'{e}lec finite element space KW - Error estimate AB - In this paper, we present a discontinuous Galerkin (DG) method based on the N\'{e}d\'{e}lec finite element space for solving a fourth-order curl equation arising from a magnetohydrodynamics model on a 3-dimensional bounded Lipschitz polyhedron. We show that the method has an optimal error estimate for a model problem involving a fourth-order curl operator. Furthermore, some numerical results in 2 dimensions are presented to verify the theoretical results.
Qingguo Hong, Jun Hu, Shi Shu & Jinchao Xu. (1970). A Discontinuous Galerkin Method for the Fourth-Order Curl Problem. Journal of Computational Mathematics. 30 (6). 565-578. doi:10.4208/jcm.1206-m3572
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