Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

Abstract

The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important open problems in these fields are discussed. The exposition concentrates on $$H^1$$ -conforming finite elements.