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 

机构地区：[1]Department of Computer Engineering,Jackson State University,Jackson,MS 39217,USA

出　　处：《Communications in Computational Physics》2012年第5期1503-1524,共22页计算物理通讯（英文）

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.

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 equations.In the extension,the treatment of the diffusive flux is exactly the same as that for the advective flux.Thanks 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 interface.As 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 crime”problem when traditional DG methods are applied to diffusion problems.For this reason,DG-CVS is conceptually simpler than other existing DG-typed methods.The 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 degrees.For even-degree polynomials,the convergence order is sub-optimal for the solution and optimal for the solution gradients.The same odd-even behaviour can also be seen in some other DG-typed methods.

关 键 词：High-order method space-time method discontinuous Galerkin(DG)method cellvertex scheme(CVS) diffusion equations 

分 类 号：O17[理学—数学]