We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamlessly build-in many standard and well-studied stabilisation techniques that can be framed as either generalised Galerkin methods, or Petrov-Galerkin methods. The framework is subsequently applied to the case of Streamine Upwind/Petrov Galerkin (SUPG) stabilisation of advection-dominated problems with small stochastic perturbations of the transport field. The norm-stability properties of two time discretisations are analysed. Numerical experiments confirm that the stabilising properties of the SUPG method naturally carry over to the DLR framework.
Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems
Chongqing Jiaotong University（重庆交通大学）；Texas A&M International University（德州农工国际大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Wayne State University（韦恩州立大学）
Residual-based stabilized reduced-order models of the transient convection-diffusion-reaction equation obtained through discrete and continuous projection
Modeling and Stabilization of Transport-Dominated Flows
NJIT（新泽西理工学院）；Western University（韦仕敦大学）；Purdue University（普渡大学）；U. of Houston（休斯顿大学）；NC State University（北卡罗来纳州立大学）；U. of Arizona（亚利桑那大学）；U. of Pittsburgh（匹兹堡大学）；U. of Tennessee（田纳西大学）；San Diego State University（圣地亚哥州立大学）
Physics-informed post-processing of stabilized finite element solutions for transient convection-dominated problems
Department of Computer Technologies, Antalya Bilim University（安塔利亚比林大学计算机技术系）；Institute of Applied Mathematics, Middle East Technical University（中东技术大学应用数学研究所）；Department of Mathematics, Indian Institute of Technology Guwahati（印度理工学院古瓦哈提数学系）
