A NEW DIRECT DISCONTINUOUS GALERKIN METHOD WITH SYMMETRIC STRUCTURE FOR NONLINEAR DIFFUSION EQUATIONS

作     者：Chad Vidden Jue Yan 

作者机构：Department of Mathematics Iowa State University Ames IA USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2013年第31卷第6期

页      面：638-662页

核心收录：

学科分类：07[理学] 080103[工学-流体力学] 08[工学] 080104[工学-工程力学] 070104[理学-应用数学] 081502[工学-水力学及河流动力学] 0815[工学-水利工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：国家自然科学基金 

主　　题：Discontinuous Galerkin Finite Element method Diffusion equation Stability,Convergence. 

摘      要：In this paper we continue the study of discontinuous Galerkin finite element methods for nonlinear diffusion equations following the direct discontinuous Galerkin （DDG） meth- ods for diffusion problems [17] and the direct discontinuous Galerkin （DDG） methods for diffusion with interface corrections [18]. We introduce a numerical flux for the test func- tion, and obtain a new direct discontinuous Galerkin method with symmetric structure. Second order derivative jump terms are included in the numerical flux formula and explicit guidelines for choosing the numerical flux are given. The constructed scheme has a sym- metric property and an optimal L2 （L2） error estimate is obtained. Numerical examples are carried out to demonstrate the optimal （k ＋ 1）th order of accuracy for the method with pk polynomial approximations for both linear and nonlinear problems, under one-dimensional and two-dimensional settings.