Superconvergence Analysis of the Runge-Kutta Discontinuous Galerkin Method with Upwind-Biased Numerical Flux for Two-Dimensional Linear Hyperbolic Equation  

作　　者：Yuan Xu Qiang Zhang 

机构地区：[1]Department of Mathematics,Nanjing University,Nanjing 210093,Jiangsu,China

出　　处：《Communications on Applied Mathematics and Computation》2022年第1期319-352,共34页应用数学与计算数学学报（英文）

基　　金：Yuan Xu is supported by the NSFC Grant 11671199;Qiang Zhang is supported by the NSFC Grant 11671199.

摘　　要：In this paper,we shall establish the superconvergence properties of the Runge-Kutta dis-continuous Galerkin method for solving two-dimensional linear constant hyperbolic equa-tion,where the upwind-biased numerical flux is used.By suitably defining the correction function and deeply understanding the mechanisms when the spatial derivatives and the correction manipulations are carried out along the same or different directions,we obtain the superconvergence results on the node averages,the numerical fluxes,the cell averages,the solution and the spatial derivatives.The superconvergence properties in space are pre-served as the semi-discrete method,and time discretization solely produces an optimal order error in time.Some numerical experiments also are given.

关 键 词：Runge-Kutta discontinuous Galerkin method Upwind-biased flux Superconvergence analysis Hyperbolic equation Two dimensions 

分 类 号：O17[理学—数学]