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The eigenvalues and eigenspaces of some discrete div- and curl-related operators. (English) Zbl 1038.65118

The paper deals with the eigenvalues and eigenspaces of some discrete div- and curl-related operators. The discrete operators give some good analogues of the continuous counterparts and play an importent role in developing finite volume schemes for solving div-curl equations and electromagnetics systems. Knowledge of the eigenvalues and eigenspaces is very useful in the numerical analysis of finite volume methods for electromagnetic systems in nonhomegeneous media.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35P15 Estimates of eigenvalues in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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