A new family of mixed finite elements in IR3
Numerische Mathematik
On the numerical integration of ordinary differential equations by symmetric composition methods
SIAM Journal on Scientific Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Multigrid Method for Maxwell's Equations
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
An Improved Algebraic Multigrid Method for Solving Maxwell's Equations
SIAM Journal on Scientific Computing
Interior penalty method for the indefinite time-harmonic Maxwell equations
Numerische Mathematik
Optimal Strong-Stability-Preserving Time-Stepping Schemes with Fast Downwind Spatial Discretizations
Journal of Scientific Computing
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
hpGEM---A software framework for discontinuous Galerkin finite element methods
ACM Transactions on Mathematical Software (TOMS)
Journal of Scientific Computing
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Nodal discontinuous Galerkin methods on graphics processors
Journal of Computational Physics
Numerical Integration of Damped Maxwell Equations
SIAM Journal on Scientific Computing
Composition Methods, Maxwell's Equations, and Source Terms
SIAM Journal on Numerical Analysis
Causal-Path Local Time-Stepping in the discontinuous Galerkin method for Maxwell's equations
Journal of Computational Physics
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This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method (DG-FEM) and the H(curl)-conforming FEM. For the spatial discretisation, hierarchic H(curl)-conforming basis functions are used up to polynomial order p=3 over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.