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Volume 19, Issue 5
Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems

Binjie Li, Xiaoping Xie & Shiquan Zhang

DOI: 10.4208/cicp.scpde14.38s

Commun. Comput. Phys., 19 (2016), pp. 1435-1460.

Published online: 2018-04

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  • Abstract

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also are applied to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

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@Article{CiCP-19-1435, author = {Binjie Li, Xiaoping Xie and Shiquan Zhang}, title = {Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1435--1460}, abstract = {

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also are applied to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.38s}, url = {http://global-sci.org/intro/article_detail/cicp/11137.html} }
TY - JOUR T1 - Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems AU - Binjie Li, Xiaoping Xie & Shiquan Zhang JO - Communications in Computational Physics VL - 5 SP - 1435 EP - 1460 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.scpde14.38s UR - https://global-sci.org/intro/article_detail/cicp/11137.html KW - AB -

This paper analyzes an abstract two-level algorithm for hybridizable discontinuous Galerkin (HDG) methods in a unified fashion. We use an extended version of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of the algorithm, and show that the theoretical results also are applied to weak Galerkin (WG) methods. The main features of our analysis are twofold: one is that we only need the minimal regularity of the model problem; the other is that we do not require the triangulations to be quasi-uniform. Numerical experiments are provided to confirm the theoretical results.

Binjie Li, Xiaoping Xie and Shiquan Zhang. (2018). Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems. Communications in Computational Physics. 19 (5). 1435-1460. doi:10.4208/cicp.scpde14.38s
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