Error Control for a Class of Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws

Error Control for a Class of Runge-Kutta Discontinuous Galerkin Methods for Nonlinear Conservation Laws
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DOI：
10.1137/050624248
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发表时间：
2007-02
期刊：
SIAM J. Numer. Anal.
影响因子：
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通讯作者：
A. Dedner;C. Makridakis;Mario Ohlberger
A. Dedner;C. Makridakis;Mario Ohlberger
中科院分区：
其他
文献类型：
--
作者：
A. Dedner;C. Makridakis;Mario Ohlberger

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对任意维空间中任意阶的Runge-Kutta间断Galerkin方法（RK-DG）提出了一个后验误差估计.为了稳定的计划的一般框架的预测。最后，它是数字演示如何使用后验误差估计设计一个有效的网格自适应和梯度限制策略。数值实验表明，该格式的稳定性和效率的增益相比，均匀网格上的计算。
We propose an a posteriori error estimate for the Runge-Kutta discontinuous Galerkin method (RK-DG) of arbitrary order in arbitrary space dimensions. For stabilization of the scheme a general framework of projections is introduced. Finally it is demonstrated numerically how the a posteriori error estimate is used to design both an efficient grid adaption and gradient limiting strategy. Numerical experiments show the stability of the scheme and the gain in efficiency in comparison with computations on uniform grids.