Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates


Harutyunyan, D. and Izsák, F. and Vegt, J.J.W. van der 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

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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
Additional information:Maxwell equations; h-Adaptive methods; Implicit error estimates; Ne´de´lec edge tetrahedral elements
Copyright:© 2008 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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