Volume 39, Issue 2
Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

Qingguo Hong & Jinchao Xu

J. Comp. Math., 39 (2021), pp. 283-310.

Published online: 2020-11

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  • Abstract

In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.

  • Keywords

Uniform Stability, Uniform Error Estimate, Hybrid Discontinuous Galerkin, Weak Galerkin.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huq11@psu.edu (Qingguo Hong)

xu@math.psu.edu (Jinchao Xu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-283, author = {Hong , Qingguo and Xu , Jinchao }, title = {Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {2}, pages = {283--310}, abstract = {

In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2003-m2018-0223}, url = {http://global-sci.org/intro/article_detail/jcm/18375.html} }
TY - JOUR T1 - Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods AU - Hong , Qingguo AU - Xu , Jinchao JO - Journal of Computational Mathematics VL - 2 SP - 283 EP - 310 PY - 2020 DA - 2020/11 SN - 39 DO - http://doi.org/10.4208/jcm.2003-m2018-0223 UR - https://global-sci.org/intro/article_detail/jcm/18375.html KW - Uniform Stability, Uniform Error Estimate, Hybrid Discontinuous Galerkin, Weak Galerkin. AB -

In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.

Qingguo Hong & Jinchao Xu. (2020). Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods. Journal of Computational Mathematics. 39 (2). 283-310. doi:10.4208/jcm.2003-m2018-0223
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