We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potentially efficient computations of the factors characterising the discretised random field. The method allows to efficiently compute a low-rank approximation of the true solution, while naturally "inbuilding" the SUPG stabilisation. Standard error rates in the L2 and SUPG-norms are recovered. Numerical experiments validate the predicted rates.

翻译：本文针对随机时间依赖对流主导问题，对全离散化的流线迎风Petrov-Galerkin动力低秩（SUPG-DLR）方法进行了误差分析。时间积分方案具有类似分裂的特性，可潜在高效计算表征离散随机场的因子。该方法能在天然"内嵌"SUPG稳定化的同时，高效计算真实解的低秩近似。恢复出了L2范数和SUPG范数下的标准误差收敛阶。数值实验验证了理论预测的收敛速率。