Finite elements in computational electromagnetism
Finite elements in computational electromagnetism
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DOI：
10.1017/cbo9780511550140.004
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发表时间：
2002-01
期刊：
影响因子：
14.2
通讯作者：
R. Hiptmair
中科院分区：
文献类型：
--
作者：
R. Hiptmair
本文讨论了电磁场中线性模型问题的有限元Galerkin格式。有限元格式被引入为离散的微分形式，与微分形式演算中的麦克斯韦方程的坐标无关的表述相匹配。从理论上研究了离散解的渐近收敛问题。由于离散微分形式代表了传统拉格朗日有限元的真正推广，分析是基于对有限元理论中已有技术的明智适应。强调了不适合离散微分形式框架的有限元方案所面临的风险和困难。
This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.