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arXiv · 1406.0390

Stability of an upwind Petrov Galerkin discretization of convection diffusion equations

Snorre H. Christiansen·Tore G. Halvorsen·Torquil M. Sørensen
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Abstract

We study a numerical method for convection diffusion equations, in the regime of small viscosity. It can be described as an exponentially fitted conforming Petrov-Galerkin method. We identify norms for which we have both continuity and an inf-sup condition, which are uniform in mesh-width and viscosity, up to a logarithm, as long as the viscosity is smaller than the mesh-width or the crosswind diffusion is smaller than the streamline diffusion. The analysis allows for the formation of a boundary layer.

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Snorre H. Christiansen, Tore G. Halvorsen, Torquil M. Sørensen. 2014-06-02. Stability of an upwind Petrov Galerkin discretization of convection diffusion equations. https://arxiv.org/abs/1406.0390

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