An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
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Computer Methods in Applied Mechanics and Engineering
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SIAM Journal on Scientific and Statistical Computing
An analysis of the discontinuous Galerkin method for wave propagation problems
Journal of Computational Physics
SIAM Journal on Scientific Computing
Explicit Finite Element Methods for Symmetric Hyperbolic Equations
SIAM Journal on Numerical Analysis
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Journal of Computational Physics
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Journal of Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
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Journal of Computational and Applied Mathematics
Journal of Computational Physics
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Locally implicit discontinuous Galerkin method for time domain electromagnetics
Journal of Computational Physics
Journal of Computational Physics
High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational Physics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
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The Discontinuous Galerkin (DG) method provides a powerful tool for approximating hyperbolic problems. Here we derive a new space-time DG method for linear time dependent hyperbolic problems written as a symmetric system (including the wave equation and Maxwell's equations). The main features of the scheme are that it can handle inhomogeneous media, and can be time-stepped by solving a sequence of small linear systems resulting from applying the method on small collections of space-time elements. We show that the method is stable provided the space-time grid is appropriately constructed (this corresponds to the usual time-step restriction for explicit methods, but applied locally) and give an error analysis of the scheme. We also provide some simple numerical tests of the algorithm applied to the wave equation in two space dimensions (plus time).