Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations

Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations
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DOI：
10.1515/1569395054069017
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发表时间：
2005-04
期刊：
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影响因子：
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通讯作者：
C. Carstensen;R. Hoppe
C. Carstensen;R. Hoppe
中科院分区：
其他
文献类型：
--
作者：
C. Carstensen;R. Hoppe

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对于二维涡流方程，我们设计了一个自适应边缘有限元方法（AEFEM），保证了H（旋）-范数的全局离散误差的误差减少，从而建立自适应方案的收敛性。的误差减少属性依赖于一个剩余型后验误差估计，并证明了离散化的基础上的最低阶边缘元素的Nédélec的第一家庭。证明的主要成分是可靠性和严格的离散局部效率的估计，以及Galerkin正交的边缘元逼近。
For the 2D eddy currents equations, we design an adaptive edge finite element method (AEFEM) that guarantees an error reduction of the global discretization error in the H (curl)-norm and thus establishes convergence of the adaptive scheme. The error reduction property relies on a residual-type a posteriori error estimator and is proved for discretizations based on the lowest order edge elements of Nédélec's first family. The main ingredients of the proof are the reliability and the strict discrete local efficiency of the estimator as well as the Galerkin orthogonality of the edge element approximation.