An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
ENO schemes with subcell resolution
Journal of Computational Physics
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
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Journal of Computational Physics
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Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
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Journal of Computational Physics
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
Simple modifications of monotonicity-preserving limiters
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
A Moving Mesh Method for One-dimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
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
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Hybrid weighted essentially non-oscillatory schemes with different indicators
Journal of Computational Physics
Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations
Journal of Scientific Computing
Advances in Computational Mathematics
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In this paper, we systematically investigate adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators which were based on the troubled cell indicators studied by Qiu and Shu [J. Qiu, C.-W. Shu, A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin mehtods using weighted essentially non-osillatory limiters, SIAM J. Sci. Comput. 27 (2005) 995-1013]. The emphasis is on comparison of the performance of adaptive RKDG method using different indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. Both h-version and r-version adaptive methods are considered in the paper. The idea is to first identify ''troubled cells'' by different troubled-cell indicators, namely those cells where limiting might be needed and discontinuities might appear, then adopt an adaptive approach in these cells. A detailed numerical study in one-dimensional case is performed, addressing the issues of efficiency (less CPU cost and more accurate), non-oscillatory property, and resolution of discontinuities.