Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers
Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers
复制标题
通过拉格朗日乘子对电极中涡流问题的实际边界条件进行数值处理
DOI：
10.1090/s0025-5718-04-01680-1
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
P. Salgado
中科院分区：
文献类型：
--
作者：
A. Bermúdez;R. Rodríguez;P. Salgado
本文讨论了有界导电区域中涡流问题的有限元解，该区域被电流穿过，并受到从物理观点出发的适当边界条件的约束。两种不同的情况下被认为是取决于边界数据：输入电流密度通量或输入电流强度。前者的分析是后者的中间步骤，在实际应用中更符合实际。弱配方的磁场进行了研究，通过适当的拉格朗日乘子施加的边界条件。根据边界数据的规律性，对所得混合制剂进行分析。在每种情况下，有限元方法和误差估计证明。最后，一些数值结果来评估的方法的有效性。
This paper deals with the finite element solution of the eddy current problem in a bounded conducting domain, crossed by an electric current and subject to boundary conditions appropriate from a physical point of view. Two different cases are considered depending on the boundary data: input current density flux or input current intensities. The analysis of the former is an intermediate step for the latter, which is more realistic in actual applications. Weak formulations in terms of the magnetic field are studied, the boundary conditions being imposed by means of appropriate Lagrange multipliers. The resulting mixed formulations are analyzed depending on the regularity of the boundary data. Finite element methods are introduced in each case and error estimates are proved. Finally, some numerical results to assess the effectiveness of the methods are reported.