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Different variants of the weighted residual finite element method are used to obtain a solution for the parabolic heat equation, which is considered to be the model equation for the steady-state Navier-Stokes equations. Results show that the collocation and the least-squares variants are more suitable for first-order systems. Results also show that the Galerkin/least-squares method is more diffusive than other methods and hence gives stable solutions for a wide range of Péclet numbers.