OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS

• 来源期刊: 计算数学(英文版)
• 关键词: Edge finite element Time-harmonic Maxwell's equations
• 年，卷（期）: 2009,（5）
• 页码范围: 563-572
• 页数: 10页
• 语种: 英文
• DOI: 10.4208/jcm.2009.27.5.011

摘要

In this paper, we obtain optimal error estimates in both L2-norm and H(curl)-norm for the Nedelec edge finite element approximation of the time-harmonic Maxwell's equations on a general Lipschitz domain discretized on quasi-uniform meshes. One key to our proof is to transform the L2 error estimates into the L2 estimate of a discrete divergence-free function which belongs to the edge finite element spaces, and then use the approximation of the discrete divergence-free function by the continuous divergence-free function and a duality argument for the continuous divergence-free function. For Nedelec's second type elements, we present an optimal convergence estimate which improves the best results available in the literature.