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Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems

Part of: Numerical approximation and computational geometry Polytopes and polyhedra

Published online by Cambridge University Press:  17 May 2016

Binjie Li ,
Xiaoping Xie  and
Shiquan Zhang
Binjie Li*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
Xiaoping Xie*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
Shiquan Zhang*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
*
*Corresponding author. Email addresses:, libinjiefem@yahoo.com(B. Li), xpxie@scu.edu.cn(X. Xie), shiquanzhang@scu.edu.cn(S. Zhang)
*Corresponding author. Email addresses:, libinjiefem@yahoo.com(B. Li), xpxie@scu.edu.cn(X. Xie), shiquanzhang@scu.edu.cn(S. Zhang)
*Corresponding author. Email addresses:, libinjiefem@yahoo.com(B. Li), xpxie@scu.edu.cn(X. Xie), shiquanzhang@scu.edu.cn(S. Zhang)
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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.

Keywords

two-level algorithmhybridizable discontinuous Galerkin methodweak Galerkin methodmultigridX-Z identity

MSC classification

Secondary: 52B10: Three-dimensional polytopes 65D18: Computer graphics, image analysis, and computational geometry 68U05: Computer graphics; computational geometry 68U07: Computer-aided design
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1435 - 1460
Copyright
Copyright © Global-Science Press 2016 

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