A two-level algorithm for the weak Galerkin discretization of diffusion problems

Binjie Li; Xiaoping Xie

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arXiv · 1405.7506

A two-level algorithm for the weak Galerkin discretization of diffusion problems

Binjie Li·Xiaoping Xie

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Abstract

This paper analyzes a two-level algorithm for the weak Galerkin (WG) finite element methods based on local Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) mixed elements for two- and three-dimensional diffusion problems with Dirichlet condition. We first show the condition numbers of the stiffness matrices arising from the WG methods are of $O(h^{-2})$. We use an extended version of the Xu-Zikatanov (XZ) identity to derive the convergence of the algorithm without any regularity assumption. Finally we provide some numerical results.

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Binjie Li, Xiaoping Xie. 2014-05-29. A two-level algorithm for the weak Galerkin discretization of diffusion problems. https://arxiv.org/abs/1405.7506

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