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A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains
Joint Authors
Nkemzi, Boniface
Nkeck, Jake Léonard
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-22
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities.
In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution.
In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains.
The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions.
A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces.
Numerical experiments that validate the theoretical results are presented.
American Psychological Association (APA)
Nkemzi, Boniface& Nkeck, Jake Léonard. 2020. A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1194439
Modern Language Association (MLA)
Nkemzi, Boniface& Nkeck, Jake Léonard. A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains. Mathematical Problems in Engineering No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1194439
American Medical Association (AMA)
Nkemzi, Boniface& Nkeck, Jake Léonard. A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1194439
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1194439