Vector finite element method based on a new variational formulation for computing propagation constants is proposed. The method is free of spurious modes provided finite elements possess discrete compactness property. Convergence analysis is conducted in the framework of collectively compact operators. Key words: Maxwell's equations, waveguide eigenmodes, full-wave analysis, hp finite elements AMS subject classification: 65N30, 35L15
|
390
|
Finite element methods for Navier-Stokes equations, SpringerVerlag
– Girault, Raviart
- 1986
|
|
83
|
Mixed finite elements
– Nédélec
- 1980
|
|
69
|
Spectral Approximation of Linear Operators
– CHATELIN
- 1983
|
|
64
|
Survey lectures on the mathematical foundations of the finite element method. In The mathematical foundations of the finite element method with applications to partial differential equations (Proc
– Babuˇska, Aziz
- 1972
|
|
49
|
C.: Mixed finite elements in R 3
– Nedelec
- 1980
|
|
27
|
A new family of mixed finite elements
– Nedelec
- 1986
|
|
22
|
An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
– Alonso, Valli
- 1999
|
|
18
|
A new family of mixed finite elements in R 3
– Nédélec
- 1986
|
|
17
|
Theory of Linear Operators in Hilbert Space
– Akhiezer, Glazman
- 1993
|
|
17
|
Error bounds for the finite element method
– Babuska
- 1971
|
|
14
|
Eigenvalue Problems
– Babuska, Osborn
- 1991
|
|
13
|
A local compactness theorem for Maxwell's equations
– Weber
- 1980
|
|
12
|
Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism
– Kikuchi
- 1986
|
|
12
|
Spectral approximation for compact operators
– Osborn
- 1975
|
|
10
|
Discrete compactness and the approximation of Maxwell's equations
– MONK, DEMKOWICZ
- 2000
|
|
9
|
hp-adaptive finite elements in electromagnetics
– Vardapetyan, Demkowicz
- 1999
|
|
8
|
Initial Boundary Value Problems
– Leis
- 1986
|
|
8
|
Discrete Compactness and Fortin Operator for Edge Elements
– Boffi
- 1999
|
|
7
|
A Two-Dimensional hp-Adaptive Finite Element Package for Electromagnetics
– Rachowicz, Demkowicz
- 1998
|
|
6
|
On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems
– CAORSI, FERNANDES, et al.
- 2000
|
|
5
|
On a Discrete Compactness Property for the Nedelec Finite Elements
– Kikuchi
- 1989
|
|
5
|
Full-wave analysis of dielectric waveguides using tangential vector finite elements
– Lee, Sun, et al.
- 1991
|
|
5
|
De Rham Diagram for hp Finite Element Spaces
– Demkowicz, Monk, et al.
- 1999
|
|
4
|
A Note on the Discrete Compactness Property and the de Rham Diagram
– Boffi
- 1999
|
|
3
|
Mathematical Analysis of a Finite Element Method without Spurious Solutions for Computation of Dielectric Waveguides
– Bermúdez, Pedreira
- 1992
|
|
3
|
A note on the de Rham complex and a discrete compactness property
– Boffi
- 2001
|
|
3
|
Asymptotic Convergence in Finite and Boundary Element Methods: Part1: Theoretical Results
– Demkowicz
- 1994
|
|
2
|
Maxwell Eigenvalues and Discrete Compactness in Two Dimensions
– Schwab, Vardapetyan
- 2000
|
|
2
|
Vardapetyan L. Modelling of electromagnetic absorption/scattering problems using hp-adaptive finite elements
– Demkowicz
- 1998
|
|
2
|
A New Nonconforming Finite Element Method for the Computation of Electromagnetic Guided Waves I: Mathematical Analysis
– Joly, Poirier, et al.
- 1996
|
|
2
|
Finite Element Analysis of Lossy Dielectric Waveguide
– Lee
- 1994
|
|
2
|
hp-Adaptive Finite Element Method for Electromagnetics with Applications to Waveguiding Structures
– Vardapetyan
- 1999
|
|
2
|
Multigrid in H(div) and H(curl
– Arnold, Falk, et al.
- 1998
|
|
2
|
Vardapetyan , "Modeling of Electromagnetic Absoption/Scattering Problems Using hp-Adaptive Finite Elements
– Demkowicz, L
- 1998
|
|
1
|
Error Bounds for Finite Element
– Babuˇska
- 1971
|
|
1
|
operator and discrete compactness for edge elements
– “Fortin
- 2000
|
|
1
|
De Rham Diagram for hp Finite Element
– Demkowicz, Monk, et al.
- 2000
|
|
1
|
Discrete Compactness of the Linear Rectangular Nedelec Element", Abstracts of Presentations at
– Kikuchi
- 1999
|
|
1
|
Theoretical and Computational Aspects of Nedelec 's Edge Elements for Electromagnetics
– Kikuchi, Yamamoto, et al.
- 1998
|
|
1
|
Applied Functional Analysis for Science and Engineering
– Oden, Demkowicz
- 1996
|
|
1
|
eds.), Finite Elements for Wave Electromagnetics
– Silvester, Pelosi
- 1994
|
|
1
|
Discrete Compactness and the
– Monk, Demkowicz, et al.
|