Petrov-Galerkin Dynamical Low Rank Approximation:SUPG stabilisation of advection-dominated problems

Autor:	Nobile, Fabio, Trindade, Thomas Trigo
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis 35R60 65M60 65M12
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.01404 Zobrazit plný text záznamu View this record from Arxiv