The Discontinuous Galerkin Approximation of the Grad-Div and Curl-Curl Operators in First-Order Form Is Involution-Preserving and Spectrally Correct
DOI10.1137/23m1555235zbMath1528.65069MaRDI QIDQ6089728
Jean-Luc Guermond, Alexandre Ern
Publication date: 15 December 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
first-order systeminvolutioncurl-curl problemspectrum approximationFriedrichs systemgrad-div problem
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Electromagnetic theory (general) (78A25) Maxwell equations (35Q61) First-order hyperbolic equations (35L02)
Cites Work
- Unnamed Item
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- Interior penalty method for the indefinite time-harmonic Maxwell equations
- Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
- Discontinuous Galerkin approximation of the Laplace eigenproblem
- Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension
- Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R}^3$
- Finite element approximation of eigenvalue problems
- Finite elements in computational electromagnetism
- Finite element exterior calculus, homological techniques, and applications
- Finite Element Methods for Navier-Stokes Equations
- Magnetostatic and Electrostatic Problems in Inhomogeneous Anisotropic Media with Irregular Boundary and Mixed Boundary Conditions
- Rate of Convergence Estimates for Nonselfadjoint Eigenvalue Approximations
- Spectral Approximation for Compact Operators
- Vector potentials in three-dimensional non-smooth domains
- On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form
- Finite Element Methods for Maxwell's Equations
- Finite Elements I
- High–order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem
- Finite element quasi-interpolation and best approximation
- Discontinuous Galerkin Approximation of the Maxwell Eigenproblem
- Smoothed projections in finite element exterior calculus
- Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory
- Gauss-compatible Galerkin schemes for time-dependent Maxwell equations
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