论文标题
局部不连续的Galerkin方法，用于层适应的网格，以依赖时间依赖的奇异扰动对流扩散问题
The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems
论文作者
论文摘要
在本文中，我们将半差异化的误差分析为时间依赖的对流扩散问题的完全离散化。我们用于空间的离散化，包括一类适应层的网格，包括shishkin-type和bakhvalov-type网格以及及时的隐式$θ$ -Scheme。对于$ k $的分段张量产品的多项式，我们在某些能量规范中获得了$ k+1/2 $的均匀或几乎均匀的误差估计，并且相对于时间而言，最佳误差估计值。我们的分析基于与所使用的各向异性网格上的固定问题相关的RITZ投影的仔细近似误差估计。我们还讨论了一维情况下的改进估计，并在时间上使用不连续的Galekin离散化。进行数值实验以支持我们的理论结果。
In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a class of layer-adapted meshes including Shishkin-type and Bakhvalov-type meshes and the implicit $θ$-scheme in time. For piecewise tensor-product polynomials of degree $k$ we obtain uniform or almost uniform error estimates with respect to space of order $k+1/2$ in some energy norm and optimal error estimates with respect to time. Our analysis is based on careful approximation error estimates for the Ritz projection related to the stationary problem on the anisotropic meshes used. We discuss also improved estimates in the one-dimensional case and the use of a discontinuous Galekin discretization in time. Numerical experiments are given to support our theoretical results.
