Abstract
We present an a posteriori estimator of the error in the L2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of Nédélec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L2-orthogonal projection of the exact eigenfunction onto the curl of the Nédélec finite element space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms, and local efficiency of the error indicators is shown by using a standard bubble functions technique. The behavior of the a posteriori error estimator is illustrated on a numerical test.
Original language | English (US) |
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Pages (from-to) | 1710-1732 |
Number of pages | 23 |
Journal | IMA Journal of Numerical Analysis |
Volume | 37 |
Issue number | 4 |
DOIs | |
State | Published - Oct 1 2017 |
Externally published | Yes |