An upwind-like discontinuous Galerkin method for hyperbolic systems
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摘要
We investigate an upwind-like DG method for solving first-order hyperbolic problems written as the Friedrichs’ systems. Under certain condition, this DG scheme may be semi-explicit such that the discrete equations can be solved layer by layer. We give the stability analysis and error estimate of order k+1/2 in the DG-norm. In particular, for some hyperbolic systems, we show that the convergence rate is of order k+1 in the L2-norm if the Qk-elements are used on rectangular meshes. Finally, we provide some numerical experiments to illustrate the theoretical analysis.
论文关键词:Discontinuous Galerkin method,Friedrichs’ systems,Upwind-like scheme,Stability analysis,Optimal error estimate
论文评审过程:Available online 9 April 2013.
论文官网地址:https://doi.org/10.1016/j.amc.2013.02.076