论文标题
准蒙特卡洛和不连续的戈尔金
Quasi-Monte Carlo and discontinuous Galerkin
论文作者
论文摘要
在这项研究中，我们考虑了针对具有随机系数的椭圆形偏微分方程（PDE）的不连续性不连续的Galerkin（DG）近似的量身定制的准蒙特卡洛（QMC）库。我们考虑了输入随机场的仿射和均匀模型以及对数正态模型，并研究了QMC cubatures的使用以近似于以输入不确定性为准的PDE响应的预期值。特别是，我们证明，DG近似的QMC收敛速率的行为与选择连续有限元相同。值得注意的是，在这项工作中开发的DG的参数规则性界限也可用于其他方法，例如稀疏网格。数值结果强调了我们的分析结果。
In this study, we consider the development of tailored quasi-Monte Carlo (QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial differential equations (PDEs) with random coefficients. We consider both the affine and uniform and the lognormal models for the input random field, and investigate the use of QMC cubatures to approximate the expected value of the PDE response subject to input uncertainty. In particular, we prove that the resulting QMC convergence rate for DG approximations behaves in the same way as if continuous finite elements were chosen. Notably, the parametric regularity bounds for DG, which are developed in this work, are also useful for other methods such as sparse grids. Numerical results underline our analytical findings.
