Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations
复制标题
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
E. Burman;A. Ern
中科院分区：
文献类型：
--
作者：
E. Burman;A. Ern
分析了对流扩散方程时间离散的两阶段隐式-显式Runge-Kutta格式。空间离散化使用连续的，分段仿射有限元与元素间梯度跳跃惩罚;间断伽辽金方法也可以考虑。平流和稳定算子被显式处理，而扩散算子被隐式处理。我们的分析取决于L2能量估计的物理空间中的离散函数。我们的主要结果是稳定性和准最优误差估计光滑的解决方案下的标准双曲CFL限制的时间步长，无论是在对流为主，在扩散为主的制度。数值例子说明了理论。
We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L 2-energy estimates on discrete functions in physical space. Our main results are stability and quasi-optimal error estimates for smooth solutions under a standard hyperbolic CFL restriction on the time step, both in the advection-dominated and in the diffusion-dominated regimes. The theory is illustrated by numerical examples.