Least-squares driven stabilised finite element solution of advection-dominated flow problems

TL;DR

This paper introduces a data-driven, least-squares based method for computing stabilised coefficients in finite element solutions of advection-dominated flows, demonstrating quasi-optimal errors across various flow problems.

Contribution

It presents a novel off-line/on-line least-squares approach for stabilised coefficients, improving accuracy and computational efficiency in flow simulations.

Findings

Least-squares stabilised coefficients achieve quasi-optimal errors.

Method performs well on structured and unstructured grids.

Applicable to various flow problems including Navier-Stokes.

Abstract

In this article, we address the solution of advection-dominated flow problems by stabilised methods, by means of least-squares computed stabilised coefficients. As main methodological tool, we introduce a data-driven off-line/on-line strategy to compute them with low computational cost. We compare the errors provided by the least-squares stabilised coefficients to those provided by several previously established stabilised coefficients within the solution of advection-diffusion and Navier-Stokes flows, on structured and un-structured grids, with and Lagrange Finite Elements up to third degree of interpolation. In all tested flows the least-squares stabilised coefficients provide quasi-optimal errors. We conclude that the least-squares procedure is a rewarding procedure, worth to be applied to general stabilised solutions of general flow problems.