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

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 Péclet number at the nodes of a mesh.

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