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The author has recently introduced a method to modify the shape functions in mixed finite element methods,to treat vanishing viscosity problems such as those that appear in fluid mechanics,in a Petrov Galerkin setting.The method retains some of the good properties of Raviart-Thomas-Nedelec elements,such as the existence of commuting projections and is related to exponential fitting.The talk will present our latest results on the stability of the method.