Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell’s equations in dispersive media
Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell’s equations in dispersive media
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DOI：
10.1016/j.cma.2006.12.009
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发表时间：
2007-07
影响因子：
7.2
通讯作者：
Jichun Li
中科院分区：
文献类型：
--
作者：
Jichun Li
我们在有界三维 (3-D) 域中考虑色散介质中与时间相关的麦克斯韦方程组。针对三种最流行的色散介质模型开发了全离散混合有限元方法：即各向同性冷等离子体、一极德拜介质和两极洛伦兹介质。在解足够平滑的假设下，证明了这三种色散介质的最佳误差估计。提供了证明我们的分析合理性的数值结果。我们相信，这是首次针对用于求解色散介质中的 3-D 麦克斯韦方程组的完全离散混合有限元方法进行误差分析。
We consider the time dependent Maxwell’s equations in dispersive media in a bounded three-dimensional (3-D) domain. Fully discrete mixed finite element methods are developed for three most popular dispersive media models: i.e., the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Optimal error estimates are proved for those three dispersive media under the assumption that the solutions are smooth enough. Numerical results justifying our analysis are provided. We believe that this is the first error analysis carried out for fully discrete mixed finite element methods for solving 3-D Maxwell’s equations in dispersive media.