High-resolution solutions of nonlinear, advection-dominated problems using a generalized finite element method
Abstract
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation, which enables stabilization through an enrichment process. The presented work uses solution-tailored enrichments for the numerical solution of the one-dimensional, unsteady Burgers equation. Mainly, generalizable exponential and hyperbolic tangent enrichments effectively capture local, steep boundary layer/shock features. Results show natural alleviation of oscillations and return smooth numerical solutions over coarse grids. Additionally, significantly improved error levels are observed compared to Lagrangian finite element methods.
Cite
@article{arxiv.2110.00554,
title = {High-resolution solutions of nonlinear, advection-dominated problems using a generalized finite element method},
author = {Troy Shilt and Patrick O'Hara and Jack J. McNamara},
journal= {arXiv preprint arXiv:2110.00554},
year = {2021}
}
Comments
26 pages, 34 figures