Local Discontinuous Galerkin Methods for High-Order Time-Dependent Partial Differential Equations  

作　　者：Yan Xu Chi-Wang Shu 

机构地区：[1]Department of Mathematics,University of Science and Technology of China,Hefei,Anhui 230026,China [2]Division of Applied Mathematics,Brown University,Providence,RI 02912,USA

出　　处：《Communications in Computational Physics》2010年第1期1-46,共46页计算物理通讯（英文）

基　　金：The research of the first author is support by NSFC grant 10601055,FANEDD of CAS and SRF for ROCS SEM;The research of the second author is supported by NSF grant DMS-0809086 and DOE grant DE-FG02-08ER25863.

摘　　要：Discontinuous Galerkin (DG) methods are a class of finite element methodsusing discontinuous basis functions, which are usually chosen as piecewise polynomi-als. Since the basis functions can be discontinuous, these methods have the flexibilitywhich is not shared by typical finite element methods, such as the allowance of ar-bitrary triangulation with hanging nodes, less restriction in changing the polynomialdegrees in each element independent of that in the neighbors (p adaptivity), and localdata structure and the resulting high parallel efficiency. In this paper, we give a generalreview of the local DG (LDG) methods for solving high-order time-dependent partialdifferential equations (PDEs). The important ingredient of the design of LDG schemes,namely the adequate choice of numerical fluxes, is highlighted. Some of the applica-tions of the LDG methods for high-order time-dependent PDEs are also be discussed.

关 键 词：Discontinuous Galerkin method local discontinuous Galerkin method numerical flux STABILITY time discretization high order accuracy STABILITY error estimates 

分 类 号：O24[理学—计算数学]