A new family of mixed finite elements in IR3
Numerische Mathematik
Canonical construction of finite elements
Mathematics of Computation
Discrete compactness and the approximation of Maxwell's equations in R3
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems
SIAM Journal on Numerical Analysis
Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
SIAM Journal on Numerical Analysis
p Interpolation Error Estimates for Edge Finite Elements of Variable Order in Two Dimensions
SIAM Journal on Numerical Analysis
Quasioptimality of some spectral mixed methods
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
New A Priori FEM Error Estimates for Eigenvalues
SIAM Journal on Numerical Analysis
Discrete Compactness for the hp Version of Rectangular Edge Finite Elements
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
Optimal Error Estimation for ${\bfH}({\rmcurl})$-Conforming $p$-Interpolation in Two Dimensions
SIAM Journal on Numerical Analysis
Convergence of the Natural $hp$-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
SIAM Journal on Numerical Analysis
Convergence of the Natural $hp$-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
SIAM Journal on Numerical Analysis
Isogeometric Discrete Differential Forms in Three Dimensions
SIAM Journal on Numerical Analysis
Solving metamaterial Maxwell's equations via a vector wave integro-differential equation
Computers & Mathematics with Applications
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In this paper we prove the discrete compactness property for a wide class of $p$ finite element approximations of nonelliptic variational eigenvalue problems in two and three space dimensions. In a very general framework, we find sufficient conditions for the $p$-version of a generalized discrete compactness property, which is formulated in the setting of discrete differential forms of order $\ell$ on a polyhedral domain in $\mathbb{R}^d$ ($0Math. Z., 265 (2010), pp. 297-320]. In the case $\ell=1$ our analysis shows that several widely used families of edge finite elements satisfy the discrete compactness property in $p$ and hence provide convergent solutions to the Maxwell eigenvalue problem. In particular, Nédélec elements on triangles and tetrahedra (first and second kind) and on parallelograms and parallelepipeds (first kind) are covered by our theory.