TY - JOUR
T1 - Approximation of the Maxwell eigenvalue problem in a least-squares setting[Formula presented]
AU - Bertrand, Fleurianne
AU - Boffi, Daniele
AU - Gastaldi, Lucia
N1 - KAUST Repository Item: Exported on 2023-09-18
Acknowledgements: The author Lucia Gastaldi is member of INdAM Research group GNCS and she is partially supported by PRIN/MIUR and by IMATI/CNR.
PY - 2023/9/6
Y1 - 2023/9/6
N2 - We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalue problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equations and design a novel least-squares formulation whose minimum is attained at the solution of the system. The eigensolutions are then approximated by considering the eigenmodes of the underlying solution operator. We study the convergence of the finite element approximation and we show several numerical tests confirming that the method provides optimally convergent results when edge elements are used. It turns out that nodal elements can be successfully employed for the approximation of our problem also in the presence of singular solutions.
AB - We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalue problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equations and design a novel least-squares formulation whose minimum is attained at the solution of the system. The eigensolutions are then approximated by considering the eigenmodes of the underlying solution operator. We study the convergence of the finite element approximation and we show several numerical tests confirming that the method provides optimally convergent results when edge elements are used. It turns out that nodal elements can be successfully employed for the approximation of our problem also in the presence of singular solutions.
UR - http://hdl.handle.net/10754/691809
UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122123003486
UR - http://www.scopus.com/inward/record.url?scp=85170432282&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2023.08.010
DO - 10.1016/j.camwa.2023.08.010
M3 - Article
SN - 0898-1221
VL - 148
SP - 302
EP - 312
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
ER -