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Stable finite element schemes are developed for the solution of the equations modeling the flow of viscoelastic fluids. In contrast with classical statements of these equations, which introduce the stress as a primary variable, these schemes explicitly involve the deformation tensor and elastic energy. Energy estimates and existence of solutions to the discrete problem are established for schemes of arbitrary order without any restrictions on the time step, mesh size, or Weissenberg number. Convergence to smooth solutions is established for the classical Oldroyd–B fluid. Numerical experiments for two classical benchmark problems verify the robustness of this approach. [ABSTRACT FROM AUTHOR]