论文标题
局部不连续的Galerkin方法，用于三阶的对流扩散类型的奇异问题
Local discontinuous Galerkin method for a third order singularly perturbed problem of convection-diffusion type
论文作者
论文摘要
研究了局部不连续的Galerkin（LDG）方法，以解决对流 - 扩散类型的三阶奇异问题。基于确切解决方案的规律性假设，我们证明了几乎$ o（n^{ - （k+1/2）}）$（最多可对数因子）能量 - 均匀收敛在扰动参数中均匀地收敛。在这里，$ k \ geq 0 $是离散空间中使用的分段多项式的最大程度，而$ n $是网格元素的数量。结果对于三种类型的层适合网格有效：shishkin型，bakhvalov-shishkin型和bakhvalov型。进行数值实验以测试理论结果。
The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of the convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$ (up to a logarithmic factor) energy-norm convergence uniformly in the perturbation parameter. Here, $k\geq 0$ is the maximum degree of piecewise polynomials used in discrete space, and $N$ is the number of mesh elements. The results are valid for the three types of layer-adapted meshes: Shishkin-type, Bakhvalov-Shishkin type, and Bakhvalov-type. Numerical experiments are conducted to test the theoretical results.
