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 -