On the natural stabilization of convection dominated problems using high order Bubnov-Galerkin finite elements

Author (s): Cai, Q.; Kollmannsberger, S.; Sala-Lardies, E.; Huerta, A. and Rank, E.
Journal: Computers and Mathematics with Applications

Volume: 66, Issue 12
Pages: 2545 – 2558
Date: 2014

Abstract:
In the case of dominating convection, standard Bubnov–Galerkin finite elements are known to deliver oscillating discrete solutions for the convection–diffusion equation. This paper demonstrates that increasing the polynomial degree (p-extension) limits these artificial numerical oscillations. This is contrary to a widespread notion that an increase of the polynomial degree destabilizes the discrete solution. This treatise also provides explicit expressions as to which polynomial degree is sufficiently high to obtain stable solutions for a given Peclet number at the nodes of a mesh.

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Bibtex:

@article{Cai-CKSHR:14,
	Author = {Quanji Cai and Stefan Kollmannsberger and Esther Sala-Lardies and Antonio Huerta and Ernst Rank},
	Title = {On the natural stabilization of convection dominated problems using high order Bubnov–Galerkin finite elements },
        Fjournal = {Computers and Mathematics with Applications},
        Journal = {Comput. Math. Appl.},
	Volume = {66},
	Number = {12},
	Pages = {2545-2558},
	Year = {2014},
        Doi = {10.1016/j.camwa.2013.09.009} 
	}