The Dorodnitsyn boundary layer formulation is combined with a modified Galerkin finite element formulation and an implicit, non-iterative marching scheme to generate a computational algorithm that is both accurate and very economical. For four representative pressure gradient cases taken from the 1968 Stanford Turbulent Boundary Layer Conference the Dorodnitsyn finite element formulation is compared with a Dorodnitsyn spectral formulation and a representative finite difference package. All methods produce solutions of high accuracy but the Dorodnitsyn finite element formulation is about ten times more economical than the other methods.