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

2021/10/15 by Gang Chen, Chen, Gang, Peter Monk +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2110.07795

openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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