Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Mathematical Analysis
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Error estimates for finite element methods for scalar conservation laws
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
SIAM Journal on Scientific Computing
An unconditionally stable method for the Euler equations
Journal of Computational Physics
A discontinuous Galerkin method for the viscous MHD equations
Journal of Computational Physics
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Mixed hp-DGFEM for Incompressible Flows
SIAM Journal on Numerical Analysis
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Journal of Computational Physics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator
SIAM Journal on Numerical Analysis
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Locally divergence-free discontinuous Galerkin methods for the Maxwell equations
Journal of Computational Physics
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We use an artificial viscosity term to stabilize discontinuous Galerkin solutions of hyperbolic conservation laws in the presence of discontinuities. Viscous coefficients are selected to minimize spurious oscillations when a kinematic wave equation is subjected to piecewise constant initial data. The same strategy is used with a local linearization in more complex situations. Several one and two-dimensional flow problems illustrate performance. A shock detection scheme [L. Krivodonova, J. Xin, J.-F. Remacle, N. Chevaugeon, J.E. Flaherty, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Appl. Numer. Math. 48 (2004) 323-338] further sharpens results near discontinuities.