High-resolution solutions of nonlinear, advection-dominated problems using a generalized finite element method

Autor:	Shilt, Troy, O'Hara, Patrick, McNamara, Jack J.
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis 65M12 65M60 65N12 65N30
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages, 34 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.00554 Zobrazit plný text záznamu View this record from Arxiv