Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High accuracy numerical methods for thermally perfect gas flows with chemistry
Journal of Computational Physics
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Journal of Computational Physics
ADER finite volume schemes for nonlinear reaction--diffusion equations
Applied Numerical Mathematics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
Journal of Computational Physics
A sub-cell WENO reconstruction method for spatial derivatives in the ADER scheme
Journal of Computational Physics
The equilibrium state method for hyperbolic conservation laws with stiff reaction terms
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 extend the high order ADER finite volume schemes introduced for stiff hyperbolic balance laws by Dumbser, Enaux and Toro (J. Comput. Phys. 227:3971---4001, 2008) to nonlinear systems of advection---diffusion---reaction equations with stiff algebraic source terms. We derive a new efficient formulation of the local space-time discontinuous Galerkin predictor using a nodal approach whose interpolation points are tensor-products of Gauss---Legendre quadrature points. Furthermore, we propose a new simple and efficient strategy to compute the initial guess of the locally implicit space-time DG scheme: the Gauss---Legendre points are initialized sequentially in time by a second order accurate MUSCL-type approach for the flux term combined with a Crank---Nicholson method for the stiff source terms. We provide numerical evidence that when starting with this initial guess, the final iterative scheme for the solution of the nonlinear algebraic equations of the local space-time DG predictor method becomes more efficient. We apply our new numerical method to some systems of advection---diffusion---reaction equations with particular emphasis on the asymptotic preserving property for linear model systems and the compressible Navier---Stokes equations with chemical reactions.