Improved Least-squares Error Estimates for Scalar Hyperbolic Problems

Abstract We consider an L_2-norm least-squares principle for a scalar hyperbolic problem. A proper variational framework for the associated finite element method is developed and studied. Analysis of the discretization error based on the least-squares projection property shows a gap of one. This number cannot be improved with a standard duality argument because the least-squares dual does not possess full elliptic regularity. Using a perturbed dual problem we are able to show that the actual gap of the least-squares method in the constant convection case is not worse than 2/3.