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12005 Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates
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Harutyunyan, D. and Izsák, F. and van der Vegt, J.J.W. and Botchev, M.A. (2008) Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates. Computer methods in applied mechanics and engineering, 197 (17-18). pp. 1620-1638. ISSN 0045-7825 *** ISI Impact 3,467 ***

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Official URL: http://dx.doi.org/10.1016/j.cma.2007.12.006

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Abstract

We consider an implicit a posteriori error estimation technique for the adaptive solution of the Maxwell equations with Nédélec edge finite element methods on three-dimensional domains. On each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis. The discrete bilinear form of the local problems is shown to satisfy an inf–sup condition which ensures the well posedness of the error equations. An adaptive solution algorithm is developed based on the obtained error estimates. The performance of the method is tested on various problems including non-convex domains with non-smooth boundaries. The numerical results show that the estimated error, computed by the implicit a posteriori error estimation technique, correlates well with the actual error. On the meshes generated adaptively with the help of the error estimator, the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom. Moreover, the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes.

Item Type:Article
Research Group:EWI-MACS: Mathematics of Computational Science
Research Program:IMPACT-Mechanics of Fluids and Solids, MESA-APS: Advanced Photonic Structures
Research Project:CIPS: Computational Integrated Optics for Photonic Structures, BRICKS/MSV1: Scientific computing, NWO-RFBR: Dutch-Russian research project
Additional Information:Please note different possible spellings of the last author's name: "Botchev" or "Bochev".
ID Code:12005
Status:Published
Deposited On:22 February 2008
Refereed:Yes
International:Yes
ISI Impact Factor:3,467
More Information:statisticsmetis

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