Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2024.117495

Authors: Fabio Nobile, Thomas Trigo Trindade

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,660

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: Dynamical low rank methods for uncertainty quantification and data assimilation