Convergence analysis of symmetric dual-wind discontinuous Galerkin approximation methods for the obstacle problem
Convergence analysis of symmetric dual-wind discontinuous Galerkin approximation methods for the obstacle problem
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DOI：
10.1016/j.jmaa.2020.123840
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发表时间：
2020-05
影响因子：
1.3
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
提出并分析了求解二阶椭圆障碍问题的对称双风间断Galerkin(DG)方法。这些新的方法遵循了DG微积分框架，该框架定义了离散微分算子来代替连续微分算子来离散偏微分方程(PDE)。我们建立了线性元素和二次元素的最优优先误差估计，只要精确解足够正则。这些结果对于一些非正惩罚参数也是成立的，重点是所有内部和边界边缘的零惩罚。数值实验验证了理论结果，并对所提方法的性能进行了评估。
This paper formulates and analyzes symmetric dual-wind discontinuous Galerkin (DG) methods for second order elliptic obstacle problem. These new methods follow from the DG differential calculus framework that defines discrete differential operators to replace the continuous differential operators when discretizing a partial differential equation (PDE). We establish optimala priorierror estimates for both linear and quadratic elements provided the exact solution is sufficiently regular. These results are also shown to hold for some non-positive penalty parameters, with the emphasis on zero penalization across all interior and boundary edges. Numerical experiments are provided to validate the theoretical results and gauge the performance of the proposed methods.