full
search.png

Search

close.png

Cancel

arrow
Volume 17, Issue 5
A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem

Jie Peng, Yingying Xie, Yage Xu & Liuqiang Zhong

DOI: 10.4208/aamm.OA-2023-0101

Adv. Appl. Math. Mech., 17 (2025), pp. 1411-1429.

Published online: 2025-07

Preview Purchase PDF 86 1200

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper, we develop and analyze a weak Galerkin (WG) finite element method for solving a $H({\rm curl})$-elliptic problem. With the aid of the weak curl operator and a stabilizer term, we first design a WG discretization. Then, by using an auxiliary problem and establishing an error equation, we achieve the optimal order error estimates in both the energy norm and $L^2$ norm for the WG method. At last, we report some numerical experiments to confirm the theoretical results.

  • Keywords

$H({\rm curl})$-elliptic problem, weak Galerkin finite element method, weak curl operator, error estimate.

  • AMS Subject Headings

65N30, 65F10, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-17-1411, author = {Peng , JieXie , YingyingXu , Yage and Zhong , Liuqiang}, title = {A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {17}, number = {5}, pages = {1411--1429}, abstract = {

In this paper, we develop and analyze a weak Galerkin (WG) finite element method for solving a $H({\rm curl})$-elliptic problem. With the aid of the weak curl operator and a stabilizer term, we first design a WG discretization. Then, by using an auxiliary problem and establishing an error equation, we achieve the optimal order error estimates in both the energy norm and $L^2$ norm for the WG method. At last, we report some numerical experiments to confirm the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0101}, url = {http://global-sci.org/intro/article_detail/aamm/24286.html} }
TY - JOUR T1 - A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem AU - Peng , Jie AU - Xie , Yingying AU - Xu , Yage AU - Zhong , Liuqiang JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1411 EP - 1429 PY - 2025 DA - 2025/07 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2023-0101 UR - https://global-sci.org/intro/article_detail/aamm/24286.html KW - $H({\rm curl})$-elliptic problem, weak Galerkin finite element method, weak curl operator, error estimate. AB -

In this paper, we develop and analyze a weak Galerkin (WG) finite element method for solving a $H({\rm curl})$-elliptic problem. With the aid of the weak curl operator and a stabilizer term, we first design a WG discretization. Then, by using an auxiliary problem and establishing an error equation, we achieve the optimal order error estimates in both the energy norm and $L^2$ norm for the WG method. At last, we report some numerical experiments to confirm the theoretical results.

Peng , JieXie , YingyingXu , Yage and Zhong , Liuqiang. (2025). A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem. Advances in Applied Mathematics and Mechanics. 17 (5). 1411-1429. doi:10.4208/aamm.OA-2023-0101
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard