Least-Squares Finite Elements for Convective Transport Problems

Convective transport problems have been difficult to treat with Galerkin-type finite-element methods, and this has led to upwind Petrov-Galerkin and Taylor-Galerkin variants of the method. Here, we develop a novel approach to the problem based on a least-squares formulation for first-order systems. The method is shown to lead to a discrete problem similar to that of the Taylor-Galerkin approach and to produce excellent results for purely convective transport (infinite Peclet number) in one dimension. The further extension of the method to nonlinear problems is described and test results for a model problem given.