Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem

2016/02/01 by Daniele Boffi, Lucia Gastaldi, Boffi, Daniele +5
Computer Science · Engineering · #65N25 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1602.00675

openalex publication_date 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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