Journal of Computational Physics
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Estimation of penalty parameters for symmetric interior penalty Galerkin methods
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection
SIAM Journal on Numerical Analysis
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
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We present a new scheme, the compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with a detailed comparison to other well-accepted DG methods. The new CDG2 method is similar to the CDG method that was recently introduced in the work of Perraire and Persson for elliptic problems. One main feature of the CDG2 method is the compactness of the stencil which includes only neighboring elements, even for higher order approximation. Theoretical results showing coercivity and stability of CDG2 and CDG for the Poisson and the heat equation are given, providing computable bounds on any free parameters in the scheme. In numerical tests for an elliptic problem, a scalar convection-diffusion equation, and for the compressible Navier-Stokes equations, we demonstrate that the CDG2 method slightly outperforms similar methods in terms of $L^2$-accuracy and CPU time.