Extension of the High-Order Space-Time Discontinuous Galerkin Cell Vertex Scheme to Solve Time Dependent Diffusion Equations

作     者：Shuangzhang Tu Gordon W.Skelton Qing Pang 

作者机构：Department of Computer EngineeringJackson State UniversityJacksonMS 39217USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2012年第11卷第5期

页      面：1503-1524页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：This work is supported by the U.S.Air Force Office of Scientific Research(AFOSR)Computational Mathematics Programunder the Award No.FA9550-08-1-0122 and the Award No.FA9550-10-1-0045.The authors are also grateful to the School of Engineering and the Department of Computer Engineering at Jackson State University for their support 

主　　题：High-order method space-time method discontinuous Galerkin(DG)method cellvertex scheme(CVS) diffusion equations 

摘      要：In this paper,the high-order space-time discontinuous Galerkin cell vertex scheme(DG-CVS)developed by the authors for hyperbolic conservation laws is extended for time dependent diffusion *** the extension,the treatment of the diffusive flux is exactly the same as that for the advective *** to the Riemannsolver-free and reconstruction-free features of DG-CVS,both the advective flux and the diffusive flux are evaluated using continuous information across the cell *** a result,the resulting formulation with diffusive fluxes present is still consistent and does not need any extra ad hoc techniques to cure the common“variational crimeproblem when traditional DG methods are applied to diffusion *** this reason,DG-CVS is conceptually simpler than other existing DG-typed *** numerical tests demonstrate that the convergence order based on the L_(2)-norm is optimal,i.e.O(h^(p+1))for the solution and O(h^(p))for the solution gradients,when the basis polynomials are of odd *** even-degree polynomials,the convergence order is sub-optimal for the solution and optimal for the solution *** same odd-even behaviour can also be seen in some other DG-typed methods.