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Sharp L^∞ estimates of HDG methods for Poisson equation II: 3D

by   Gang Chen, et al.
University of Electronic Science and Technology of China
University of Delaware
Carnegie Mellon University

In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal L^∞ estimates (up to logarithmic factors) for the solution of Poisson's equation by a hybridizable discontinuous Galerkin (HDG) method. However, the estimates only work in 2D. In this paper, we obtain sharp (without logarithmic factors) L^∞ estimates for the HDG method in both 2D and 3D. Numerical experiments are presented to confirm our theoretical result.


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