The local discontinuous Galerkin method for time-dependent convection-diffusion systems
The local discontinuous Galerkin method for time-dependent convection-diffusion systems
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DOI：
10.1137/s0036142997316712
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发表时间：
1998-11-16
影响因子：
2.9
通讯作者：
Shu, CW
中科院分区：
文献类型：
--
作者：
Cockburn, B;Shu, CW
本文研究非线性、含时对流扩散方程组的局部间断Galerkin（LDG）方法。这些方法是Runge-Kutta间断Galerkin（RKDG）方法的扩展，用于纯双曲型系统对流扩散系统，并与这些方法共享其高并行性，高阶形式精度，易于处理复杂的几何对流为主的问题。证明了对于标量方程，LDG方法在非线性情形下是L-2稳定的。此外，在线性的情况下，它表明，如果多项式的次数k使用，该方法是k阶准确的一般三角剖分，虽然这个顺序的收敛是次优的，它是尖锐的LDG方法。给出了显示该方法性能的初步数值例子。
In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated problems. It is proven that for scalar equations, the LDG methods are L-2 -stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.