Inf-sup testing of upwind methods

We propose inf{sup testing for nite element methods with upwinding used to solve convection{di usion problems. The testing evaluates the stability of a method and compactly displays the numerical behaviour as the convection e ects increase. Four discretization schemes are considered: the standard Galerkin procedure, the full upwind method, the Galerkin least-squares scheme and a high-order derivative arti cial di usion method. The study shows that, as expected, the standard Galerkin method does not pass the inf{sup tests, whereas the other three methods pass the tests. Of these methods, the high-order derivative arti cial di usion procedure introduces the least amount of arti cial di usion