Discontinuous Galerkin derivative operators with applications to second‐order elliptic problems and stability
Discontinuous Galerkin derivative operators with applications to second‐order elliptic problems and stability
复制标题
不连续伽辽金导数算子及其在二阶椭圆问题和稳定性中的应用
DOI：
10.1002/mma.3440
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发表时间：
2015
影响因子：
2.9
通讯作者：
S. Wise
中科院分区：
文献类型：
--
作者：
W. Feng;T. Lewis;S. Wise
用不连续伽辽金（DG）有限元内演算作为一个通用框架，描述了二阶椭圆型问题的各种DG逼近方法。在此框架下，将对称内罚方法、局部不连续Galerkin方法和对偶风不连续Galerkin方法用原始形式表示进行比较。双风不连续伽辽金方法的无罚性质将被激发并用于更好地理解各种DG方法的解析性质。将考虑诺依曼边界条件与数值实验，以支持理论结果。将推导出许多范数等价，为双绕组技术应用于其他问题奠定基础。版权所有©2015 John Wiley & Sons， Ltd
A discontinuous Galerkin (DG) finite‐element interior calculus is used as a common framework to describe various DG approximation methods for second‐order elliptic problems. Using the framework, symmetric interior‐penalty methods, local discontinuous Galerkin methods, and dual‐wind discontinuous Galerkin methods will be compared by expressing all of the methods in primal form. The penalty‐free nature of the dual‐wind discontinuous Galerkin method will be both motivated and used to better understand the analytic properties of the various DG methods. Consideration will be given to Neumann boundary conditions with numerical experiments that support the theoretical results. Many norm equivalencies will be derived laying the foundation for applying dual‐winding techniques to other problems. Copyright © 2015 John Wiley & Sons, Ltd.