The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
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
Journal of Computational Physics
Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
SIAM Journal on Numerical Analysis
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Numerical solution of the acoustic wave equation using Raviart-Thomas elements
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
LBB stability of a mixed Galerkin finite element pair for fluid flow simulations
Journal of Computational Physics
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
Interior penalty DG methods for Maxwell's equations in dispersive media
Journal of Computational Physics
Insights from von Neumann analysis of high-order flux reconstruction schemes
Journal of Computational Physics
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
SIAM Journal on Numerical Analysis
High-order explicit local time-stepping methods for damped wave equations
Journal of Computational and Applied Mathematics
Dispersion and Dissipation Errors of Two Fully Discrete Discontinuous Galerkin Methods
Journal of Scientific Computing
General DG-Methods for Highly Indefinite Helmholtz Problems
Journal of Scientific Computing
An analysis of discretizations of the Helmholtz equation in L2 and in negative norms
Computers & Mathematics with Applications
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Discontinuous Galerkin finite element methods (DGFEM) offer certain advantages over standard continuous finite element methods when applied to the spatial discretisation of the acoustic wave equation. For instance, the mass matrix has a block diagonal structure which, used in conjunction with an explicit time stepping scheme, gives an extremely economical scheme for time domain simulation. This feature is ubiquitous and extends to other time-dependent wave problems such as Maxwell's equations. An important consideration in computational wave propagation is the dispersive and dissipative properties of the discretisation scheme in comparison with those of the original system. We investigate these properties for two popular DGFEM schemes: the interior penalty discontinuous Galerkin finite element method applied to the second-order wave equation and a more general family of schemes applied to the corresponding first order system. We show how the analysis of the multi-dimensional case may be reduced to consideration of one-dimensional problems. We derive the dispersion error for various schemes and conjecture on the generalisation to higher order approximation in space