Quasioptimality of some spectral mixed methods
Journal of Computational and Applied Mathematics
Computation of optical modes in axisymmetric open cavity resonators
Future Generation Computer Systems
On the finite element method on quadrilateral meshes
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Finite element approximation of Maxwell eigenproblems on curved Lipschitz polyhedral domains
Applied Numerical Mathematics
Some remarks on quadrilateral mixed finite elements
Computers and Structures
Nonconforming Maxwell Eigensolvers
Journal of Scientific Computing
Computation of optical modes in axisymmetric open cavity resonators
Future Generation Computer Systems
An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements
Journal of Computational Physics
Innovative mimetic discretizations for electromagnetic problems
Journal of Computational and Applied Mathematics
Numerical Simulation of Electromagnetic Solitons and Their Interaction with Matter
Journal of Scientific Computing
Error analysis of a discontinuous Galerkin method for Maxwell equations in dispersive media
Journal of Computational Physics
Numerical analysis of a PML model for time-dependent Maxwell's equations
Journal of Computational and Applied Mathematics
Discrete Compactness for the $p$-Version of Discrete Differential Forms
SIAM Journal on Numerical Analysis
Isogeometric Discrete Differential Forms in Three Dimensions
SIAM Journal on Numerical Analysis
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
Journal of Computational Physics
Mimetic scalar products of discrete differential forms
Journal of Computational Physics
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The purpose of this paper is to address some difficulties which arise in computing the eigenvalues of Maxwell's system by a finite element method. Depending on the method used, the spectrum may be polluted by spurious modes which are difficult to pick out among the approximations of the physically correct eigenvalues. Here we propose a criterion to establish whether or not a finite element scheme is well suited to approximate the eigensolutions and, in the positive case, we estimate the rate of convergence of the eigensolutions. This criterion involves some properties of the finite element space and of a suitable Fortin operator. The lowest-order edge elements, under some regularity assumptions, give an example of space satisfying the required conditions. The construction of such a Fortin operator in very general geometries and for any order edge elements is still an open problem.Moreover, we give some justification for the spectral pollution which occurs when nodal elements are used. Results of numerical experiments confirming the theory are also reported.