Eigenvalue approximation by a mixed method for resonant inhomogeneous cavities with metallic boundaries

Author:
Vincent Levillain

Journal:
Math. Comp. **58** (1992), 11-20

MSC:
Primary 65N25; Secondary 35P15, 65N30, 78A25

MathSciNet review:
1106975

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Abstract: For an inhomogeneous cavity bounded by a perfect conductor, we prove that the approximation of the eigenvalues for the Maxwell problem leads to a second-order rate of convergence when using mixed finite elements. If the cavity has a disconnected boundary, the problem has null eigenvalues. We verify the existence of null eigenvalues for the approximate problem. They do not mix with the others that still converge at the same rate.

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DOI:
https://doi.org/10.1090/S0025-5718-1992-1106975-3

Article copyright:
© Copyright 1992
American Mathematical Society