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Volume 41, Issue 2
The a Posteriori Error Estimator of SDG Method for Variable Coefficients Time-Harmonic Maxwell's Equations

Wei Yang, Xin Liu, Bin He & Yunqing Huang

DOI: 10.4208/jcm.2112-m2020-0330

J. Comp. Math., 41 (2023), pp. 263-286.

Published online: 2022-11

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  • Abstract

In this paper, we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations. We propose two a posteriori error estimators, one is the recovery-type estimator, and the other is the residual-type estimator. We first propose the curl-recovery method for the staggered discontinuous Galerkin method (SDGM), and based on the super-convergence result of the postprocessed solution, an asymptotically exact error estimator is constructed. The residual-type a posteriori error estimator is also proposed, and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's equations. The efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.

  • Keywords

Maxwell’s equations, A posteriori error estimation, Staggered discontinuous Galerkin.

  • AMS Subject Headings

65N30, 65F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangweixtu@126.com (Wei Yang)

xincherry05@163.com (Xin Liu)

Hebinxtu@126.com (Bin He)

huangyq@xtu.edu.cn (Yunqing Huang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-263, author = {Yang , WeiLiu , XinHe , Bin and Huang , Yunqing}, title = {The a Posteriori Error Estimator of SDG Method for Variable Coefficients Time-Harmonic Maxwell's Equations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {2}, pages = {263--286}, abstract = {

In this paper, we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations. We propose two a posteriori error estimators, one is the recovery-type estimator, and the other is the residual-type estimator. We first propose the curl-recovery method for the staggered discontinuous Galerkin method (SDGM), and based on the super-convergence result of the postprocessed solution, an asymptotically exact error estimator is constructed. The residual-type a posteriori error estimator is also proposed, and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's equations. The efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2112-m2020-0330}, url = {http://global-sci.org/intro/article_detail/jcm/21180.html} }
TY - JOUR T1 - The a Posteriori Error Estimator of SDG Method for Variable Coefficients Time-Harmonic Maxwell's Equations AU - Yang , Wei AU - Liu , Xin AU - He , Bin AU - Huang , Yunqing JO - Journal of Computational Mathematics VL - 2 SP - 263 EP - 286 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2112-m2020-0330 UR - https://global-sci.org/intro/article_detail/jcm/21180.html KW - Maxwell’s equations, A posteriori error estimation, Staggered discontinuous Galerkin. AB -

In this paper, we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations. We propose two a posteriori error estimators, one is the recovery-type estimator, and the other is the residual-type estimator. We first propose the curl-recovery method for the staggered discontinuous Galerkin method (SDGM), and based on the super-convergence result of the postprocessed solution, an asymptotically exact error estimator is constructed. The residual-type a posteriori error estimator is also proposed, and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's equations. The efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.

Wei Yang, Xin Liu, Bin He & Yunqing Huang. (2022). The a Posteriori Error Estimator of SDG Method for Variable Coefficients Time-Harmonic Maxwell's Equations. Journal of Computational Mathematics. 41 (2). 263-286. doi:10.4208/jcm.2112-m2020-0330
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