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 N´ed´elec 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.
Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem
Gastaldi, Lucia;
2017-01-01
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 N´ed´elec 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
