Data-driven stabilized finite element solution of advection-dominated flow problems

In this article, we address the solution of advection-dominated flow problems by stabilized methods, by means of data-driven least-squares computed stabilized 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 data-driven stabilized coefficients to those provided by several previously established stabilized coefficients within the solution of advection- diffusion and Navier-Stokes flows, on structured and un-structured grids, with Lagrange Finite Elements up to third degree of interpolation. We obtain substantial error improvements for high-order finite element interpolation. We conclude that the data-driven procedure is a rewarding procedure, worth to be applied to general stabilized solutions of general flow problems.