Work

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

Year: 2016

Type: preprint

Abstract: We present an a posteriori estimator of the error in the L^2-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 L^2-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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1602.00675

Authors: Boffi, Daniele, Gastaldi, Lucia, Rodríguez, Rodolfo, Šebestová, Ivana

Institutions: University of Pavia, University of Brescia, University of Concepción

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Universidad de Chile, Gruppo Nazionale per il Calcolo Scientifico, Comisión Nacional de Investigación Científica y Tecnológica

Awards: G25078073, G5136694873

OpenAlex ID: W2253424263

Cites: 12

Cited by: 2

Related to: 20