The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
On some aspects of the discontinuous Galerkin finite element method for conservation laws
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics
Solving the euler equations on graphics processing units
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Compact and Stable Discontinuous Galerkin Methods for Convection-Diffusion Problems
SIAM Journal on Scientific Computing
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In this paper we present a stabilized Discontinuous Galerkin (DG) method for hyperbolic and convection dominated problems. The presented scheme can be used in several space dimension and with a wide range of grid types. The stabilization method preserves the locality of the DG method and therefore allows to apply the same parallelization techniques used for the underlying DG method. As an example problem we consider the Euler equations of gas dynamics for an ideal gas. We demonstrate the stability and accuracy of our method through the detailed study of several test cases in two space dimension on both unstructured and cartesian grids. We show that our stabilization approach preserves the advantages of the DG method in regions where stabilization is not necessary. Furthermore, we give an outlook to adaptive and parallel calculations in 3d.