A posteriori error estimates for Maxwell equations
A posteriori error estimates for Maxwell equations
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DOI：
10.1090/s0025-5718-07-02030-3
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发表时间：
2008-01-01
影响因子：
2
通讯作者：
Schoeberl, Joachim
中科院分区：
文献类型：
--
作者：
Schoeberl, Joachim
将Maxwell方程作为函数空间H（旋度）中的变分边值问题，用Nedelec有限元进行离散。Beck et al.， 2000提出了一种残差型后验误差估计器，并在一定条件下对其进行了分析。在本文中，我们证明了该误差估计在Lipschitz域上的可靠性。关键是为J. Schoberl《混合有限元的可交换拟插值算子》中引入的可交换拟插值算子建立新的误差估计。对于加性Schwarz预处理也需要类似的估计。为了结合边界条件，我们建立了一个新的推广结果。
Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nedelec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish new error estimates for the commuting quasi-interpolation operators recently introduced in J. Schoberl, Commuting quasi-interpolation operators for mixed finite elements. Similar estimates are required for additive Schwarz preconditioning. To incorporate boundary conditions, we establish a new extension result.