Journal of Computational Physics
A well-behaved TVD limiter for high-resolution calculations of unsteady flow
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Journal of Computational Physics
Fast high order ADER schemes for linear hyperbolic equations
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
ADER schemes on adaptive triangular meshes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
Journal of Computational Physics
On Source Terms and Boundary Conditions Using Arbitrary High Order Discontinuous Galerkin Schemes
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
Nonuniform time-step Runge-Kutta discontinuous Galerkin method for Computational Aeroacoustics
Journal of Computational Physics
Comparison of solvers for the generalized Riemann problem for hyperbolic systems with source terms
Journal of Computational Physics
Journal of Computational Physics
A two-dimensional fourth-order unstructured-meshed Euler solver based on the CESE method
Journal of Computational Physics
Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes
Journal of Computational Physics
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In this article we propose the use of the ADER methodology of solving generalized Riemann problems to obtain a numerical flux, which is high order accurate in time, for being used in the Discontinuous Galerkin framework for hyperbolic conservation laws. This allows direct integration of the semi-discrete scheme in time and can be done for arbitrary order of accuracy in space and time. The resulting fully discrete scheme in time does not need more memory than an explicit first order Euler time-stepping scheme. This becomes possible because of an extensive use of the governing equations inside the numerical scheme itself via the so-called Cauchy---Kovalewski procedure. We give an efficient algorithm for this procedure for the special case of the nonlinear two-dimensional Euler equations. Numerical convergence results for the nonlinear Euler equations results up to 8th order of accuracy in space and time are shown