The Direct Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Marching for Linear Convection-Diffusion Problems
The Direct Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Marching for Linear Convection-Diffusion Problems
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DOI：
10.1007/s42967-020-00114-1
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发表时间：
2021-04
影响因子：
1.6
通讯作者：
Haijin Wang;Qiang Zhang
中科院分区：
文献类型：
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作者：
Haijin Wang;Qiang Zhang
本文对求解一维线性对流扩散问题的Runge-Kutta型隐-显时间推进直接间断Galerkin（DDG）方法进行了全离散稳定性分析。在空间离散中，既考虑了原始DDG方法，也考虑了带界面修正的精化DDG方法。在时间离散中，对流项被显式处理，扩散项被隐式处理。通过能量方法，我们证明了相应的全离散格式是无条件稳定的，即时间步长的上界只需要一个与网格尺寸无关的常数.借助于一种特殊的全局投影，得到了最优误差估计。数值实验验证了格式的稳定性和精度。
In this paper, a fully discrete stability analysis is carried out for the direct discontinuous Galerkin (DDG) methods coupled with Runge-Kutta-type implicit-explicit time marching, for solving one-dimensional linear convection-diffusion problems. In the spatial discretization, both the original DDG methods and the refined DDG methods with interface corrections are considered. In the time discretization, the convection term is treated explicitly and the diffusion term implicitly. By the energy method, we show that the corresponding fully discrete schemes are unconditionally stable, in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh sizeh. Optimal error estimate is also obtained by the aid of a special global projection. Numerical experiments are given to verify the stability and accuracy of the proposed schemes.