Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要Local discontinuous Galerkin (LDG) methods are popular for convection–diffusion equations. In LDG methods, we introduce an auxiliary variable p to represent the derivative of the primary variable u, and solve them on the same mesh. In this paper, we will introduce a new LDG method, and solve u and p on different meshes. The stability and error estimates will be investigated. The new algorithm is more flexible and flux-free for pure diffusion equations without introducing additional computational cost compared with the original LDG methods, since it is not necessary to solve each equation twice. Moreover, it is possible to construct third-order maximum-principle-preserving schemes based on the new algorithm. However, one cannot anticipate optimal accuracy in some special cases. In this paper, we will find out the reason for accuracy degeneration which further leads to several alternatives to obtain optimal convergence rates. Finally, several numerical experiments will be given to demonstrate the stability and optimal accuracy of the new algorithm.
著者Jie Du, Yang Yang, Eric Chung
期刊名稱BIT Numerical Mathematics
出版年份2019
月份12
卷號59
期次4
頁次853 - 876
國際標準期刊號0006-3835
語言美式英語

上次更新時間 2020-14-09 於 00:14