On the application of a least squares residual-fitting finite element formulation to fluid flow problems

The connection between the least squares residual fitting finite element formulation and reduced integration is considered for two model problems, one of which requires an isoparametric mapping. For both problems a significant improvement in accuracy is achieved when compared with a conventional Galerkin finite element formulation. It is found that the two methods are equivalent for rectangular elements as long as an isoparametric mapping is not required. For triangular elements there is no direct link between the two methods and neither method produces any significant improvement over the use of exact numerical integration.