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

作     者：Qiang Du Lili Ju Jianfang Lu Xiaochuan Tian Qiang Du;Lili Ju;Jianfang Lu;Xiaochuan Tian

作者机构：Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkNY 10027USA Department of MathematicsUniversity of South CarolinaColumbiaSC 29208USA South China Research Center for Applied Mathematics and Interdisciplinary StudiesSouth China Normal UniversityGuangzhou 510631China Department of MathematicsUniversity of Texas at AustinAustinTX 78712USA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2020年第2卷第1期

页      面：31-55页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Q.Du’s research is partially supported by US National Science Foundation Grant DMS-1719699 US AFOSR MURI Center for Material Failure Prediction Through Peridynamics and US Army Research Office MURI Grant W911NF-15-1-0562.L.Ju’s research is partially supported by US National Science Foundation Grant DMS-1818438.J.Lu’s research is partially supported by Postdoctoral Science Foundation of China Grant 2017M610749.X.Tian’s research is partially supported by US National Science Foundation Grant DMS-1819233 

主　　题：Nonlocal diff usion Discontinuous Galerkin method Interior penalty Asymptotic compatibility Strong stability preserving 

摘      要：There have been many theoretical studies and numerical investigations of nonlocal diffusion(ND)problems in recent *** 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 *** show that the proposed discontinuous Galerkin scheme is stable and ***,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 *** tests are also presented to demonstrate the eff ectiveness and the robustness of the proposed method.