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Sharp $L^\infty$ estimates of HDG methods for Poisson equation II: 3D (2110.07795v1)
Published 15 Oct 2021 in math.NA and cs.NA
Abstract: In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal $L\infty$ 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) $L\infty$ estimates for the HDG method in both 2D and 3D. Numerical experiments are presented to confirm our theoretical result.