Summary. The present paper deals with the mathematical and numerical analysis of evolution problems in nonlinear small strains viscoelasticity of Burger's type. After a brief review of the mechanical model, the viscoelastic problem to be solved is written as an abstract evolution problem. The associated operator is proved to be maximal monotone, thus implying existence and uniqueness of solutions. This problem is then solved numerically by a backward Euler discretization in time, a finite element approximation in space and by using a preconditioned conjugate gradient algorithm for solving the resulting nonlinear algebraic systems. Numerical results are finally presented to illustrate the solution procedure.

During the European project ADIGMA (Adaptive Higher-Order Variational Methods for Aerodynamic Application in Industry) Dassault Aviation extended its stabilized finite element industrial Navier-Stokes code AeTher to higher-order elements. The high-order approach (3 rd and 4 th order) was carefully assessed using inviscid subsonic and transonic, laminar, and high Reynolds number turbulent flows. First results on a full aircraft configuration were also achieved [3]. They showed that spurious drag was considerably reduced by the use of higher-order elements.In this paper, we focus on the application of higher-order elements to Large Eddy Simulation. We revisit the results of [1] where a careful second-order accurate LES model was introduced. At that time we established that second-order accuracy was sufficient for the practical utilization of LES in the industry. Today the industrial applications of LES and DES are numerous (see [2] and Fig. 1). We reconsider the use of these models in the light of higher-order elements, possibly reducing the number of grid points required per wave length and increasing the number of resolved scales for a given grid size.We reconsider the DES of the flow past the QinetiQ M219 open cavity at a transonic Mach number. In Figure 2, we compare the results obtained with the original secondorder accurate linear elements against third-order accurate quadratic elements. In both instances time integration is provided by a standard second-order accurate backward difference scheme. Both meshes contain the exact same number of degrees of freedom. One can notice a more rapid transition to 3-D flow and finer turbulent structures in the higher-order solution. Early analysis suggests that higher-order elements reveal the limits of simple subgrid-scale models, such as the underlying Smagorinsky model in DES, in a stronger way than mesh refinement with standard second-order elements. The impact of

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