Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
复制标题
用于解决平稳输运问题的自动稳定不连续 Petrov-Galerkin 方法：准最优测试空间范数
DOI：
10.1016/j.camwa.2013.07.016
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
V. Calo
中科院分区：
文献类型：
--
作者：
A. Niemi;N. Collier;V. Calo
研究了间断Petrov-Galerkin（DPG）有限元框架在定常对流扩散问题中的应用。特别是，我们演示了如何准最优的测试空间范数提高了DPG方法的鲁棒性消失扩散。我们数值比较粗网格精度的近似时，使用准最佳的规范，标准规范，加权规范。我们的研究结果表明，准最优范数导致更准确的结果在两个空间维度上的三个基准问题。我们解决的问题的决议的最佳测试功能方面的准最佳的规范，通过研究其收敛性数值。为了便于理解的方法，我们还包括从算法的角度详细解释的方法。
We investigate the application of the discontinuous Petrov–Galerkin (DPG) finite element framework to stationary convection–diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view.