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OPTIMAL ERROR ESTIMATES FOR NEDELEC EDGE ELEMENTS FOR TIME-HARMONIC MAXWELL'S EQUATIONS |
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| Authors: | Liuqiang Zhong Shi Shu School of Mathematical Computational Sciences Xiangtan University Xiangtan China Gabriel Wittum Simulation Modelling Goethe-Center for Scientic Computing Goethe-University Kettenhofweg Frankfurt am Main Germany Jinchao Xu |
| Institution: | Liuqiang Zhong Shi Shu School of Mathematical , Computational Sciences,Xiangtan University,Xiangtan 411105,China Gabriel Wittum Simulation , Modelling Goethe-Center for Scientic Computing,Goethe-University,Kettenhofweg 139,60325 Frankfurt am Main,Germany Jinchao Xu Department of Mathematics,Pennsylvania State University,University Park,PA 16802,USA |
| Abstract: | In this paper, we obtain optimal error estimates in both L~2-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 L~2 error estimates into the L~2 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... |
| Keywords: | Edge finite element Time-harmonic Maxwell's equations |
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