首页> 外文会议>GAMM Workshop on Computational Electromagnetics; 20010126-20010128; Kiel; DE >Finite Elements for the Time Harmonic Maxwell's Equations
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Finite Elements for the Time Harmonic Maxwell's Equations

机译:时间调和麦克斯韦方程组的有限元

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We review the time harmonic Maxwell's system and its approximation via the finite element method. The problem under consideration is strictly related to the so-called interior Maxwell's eigenproblem. Standard nodal (Lagrangian) elements are known to provide useless results on general meshes. Special two-dimensional meshes have been shown to give good results, but the use of them is not recommended. The use of a penalty strategy with nodal elements has been proved to give wrong results for domains with singularities. Some special schemes, which make use of nodal elements, circumvent this problem; one of them is described in this paper. On the other hand the so-called edge elements represent the natural choice. A new proof of convergence for a method based on edge elements is summarized.
机译:我们通过有限元方法回顾了时间谐波麦克斯韦系统及其近似。正在考虑的问题与所谓的麦克斯韦内部特征问题严格相关。已知标准节点(拉格朗日)元素在普通网格上无法提供有用的结果。特殊的二维网格已显示出良好的效果,但不建议使用它们。事实证明,使用带有节点元素的惩罚策略会给具有奇异域的域提供错误的结果。一些利用节点元素的特殊方案规避了这个问题。本文描述了其中之一。另一方面,所谓的边缘元素代表自然的选择。总结了一种新的基于边缘元素的收敛性证明。

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