Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs
Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs
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DOI：
10.58997/ejde.conf.26.l1
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发表时间：
2022-08
影响因子：
0.7
通讯作者：
T. Lewis;Aaron Rapp;Yi Zhang
中科院分区：
文献类型：
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作者：
T. Lewis;Aaron Rapp;Yi Zhang
本文分析了用于逼近二阶椭圆型偏微分方程（PDE）的对称双迎风间断伽辽金（DWDG）方法中惩罚参数的影响。DWDG方法源自DG微积分框架，该框架定义了在离散化PDE时用于替代连续微分算子的离散微分算子。我们证明了当惩罚参数趋于无穷大时，DWDG逼近收敛于连续伽辽金逼近。我们还针对椭圆型二阶PDE解的正则性，测试了其对惩罚参数与DWDG逼近误差之间关系的影响。文中提供了数值实验以验证理论结果，并研究惩罚参数与L² -误差之间的关系。更多信息见https://ejde.math.txstate.edu/conf - proc/26/l1/abstr.html
This article analyzes the effect of the penalty parameter used in symmetric dual-wind discontinuous Galerkin (DWDG) methods for approximating second order elliptic partial differential equations (PDE). DWDG methods follow from the DG differential calculus framework that defines discrete differential operators used to replace the continuous differential operators when discretizing a PDE. We establish the convergence of the DWDG approximation to a continuous Galerkin approximation as the penalty parameter tends towards infinity. We also test the influence of the regularity of the solution for elliptic second-order PDEs with regards to the relationship between the penalty parameter and the error for the DWDG approximation. Numerical experiments are provided to validate the theoretical results and to investigate the relationship between the penalty parameter and the L^2-error. For more information see https://ejde.math.txstate.edu/conf-proc/26/l1/abstr.html