Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

TL;DR

This paper provides an error analysis for a SUPG-stabilised dynamical low-rank approximation method applied to random advection-dominated problems, demonstrating standard error rates and validating through numerical experiments.

Contribution

It introduces an error analysis for a fully discretised SUPG-DLR method, combining stabilization with low-rank approximation for efficient computation.

Findings

Standard error rates in L2 and SUPG-norms are achieved.

Numerical experiments confirm theoretical error estimates.

Method enables efficient low-rank approximation of solutions.

Abstract

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.