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. Numerical results underline our analytical findings.

翻译：在这项研究中,我们考虑为不符合不连续的加勒金(DG)等离子体部分偏差方程式近似随机系数,开发量身定制的准蒙特卡洛(QMC)幼崽。我们考虑输入随机字段的方形和统一模型以及逻辑正常模型,并调查QMC幼崽的使用情况,以近似PDE反应的预期值,但须视投入的不确定性而定。特别是,我们证明由此产生的QMC差分体近差方程式的趋同率与选择连续的有限要素相同。数字结果突显了我们的分析结论。