A Discontinuous Galerkin Method with Penalty for One-Dimensional Nonlocal Diffusion Problems

• 作者: Jianfang Lu Lili Ju Qiang Du Xiaochuan Tian
• 来源期刊: 应用数学与计算数学学报(英文)
• 学科: 数学
• 关键词: NONLOCAL diff usion DISCONTINUOUS GALERKIN method Interior PENALTY ASYMPTOTIC compatibility Strong stability PRESERVING
• 年，卷（期）: 2020,（1）
• 页码范围: 31-55
• 页数: 25页
• 分类号: O17

摘要

There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent years.In this paper,we propose and analyze a new discontinuous Galerkin method for solving one-dimensional steady-state and time-dependent ND problems,based on a formulation that directly penalizes the jumps across the element interfaces in the nonlocal sense.We show that the proposed discontinuous Galerkin scheme is stable and convergent.Moreover,the local limit of such DG scheme recovers classical DG scheme for the corresponding local diff usion problem,which is a distinct feature of the new formulation and assures the asymptotic compatibility of the discretization.Numerical tests are also presented to demonstrate the eff ectiveness and the robustness of the proposed method.