ncku-talk2010-10-07

NCTS(South)/ NCKU Math Colloquium

DATE 2010-10-07　14:00-15:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 邱建賢教授（南京大學數學系）

TITLE Adaptive RKDG methods with different indicators

ABSTRACT In this presentation, 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 [SIAM J. Sci. Comput., 27 (2005), 995-1013], 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 CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.

NCTS(South)/ NCKU Math Colloquium

DATE	2010-10-07　14:00-15:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	邱建賢教授（南京大學數學系）

TITLE	Adaptive RKDG methods with different indicators

ABSTRACT	In this presentation, 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 [SIAM J. Sci. Comput., 27 (2005), 995-1013], 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 CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.