Stability of an upwind Petrov Galerkin discretization of convection diffusion equations
Numerical Analysis
2016-02-23 v2
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.
Keywords
Cite
@article{arxiv.1406.0390,
title = {Stability of an upwind Petrov Galerkin discretization of convection diffusion equations},
author = {Snorre H. Christiansen and Tore G. Halvorsen and Torquil M. Sørensen},
journal= {arXiv preprint arXiv:1406.0390},
year = {2016}
}
Comments
v1: 18 pages. 2 figures. v2: 22 pages. Numerous details added and completely rewritten final proof. 8 pages appendix with old proof