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arXiv · 1502.04371

Analysis of a two-level algorithm for HDG methods for diffusion problems

Binjie Li·Xiaoping Xie·Shiquan 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 apply 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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Binjie Li, Xiaoping Xie, Shiquan Zhang. 2015-02-15. Analysis of a two-level algorithm for HDG methods for diffusion problems. https://doi.org/10.4208/cicp.scpde14.19s

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