Adaptive hp-finite element viscoelastic flow calculations

Accuracy and stability remain key issues in viscoelastic flow simulation. Classical low-order finite element techniques fail to converge when the elasticity of the fluid is increased. In this paper, an adaptive hp-finite element method is used to solve differential viscoelastic flow problems. An a posteriori error estimator, based on some recent rigorous results of Oden and Wu for the Navier-Stokes equations ([1]) is also used. Starting from an initial mesh, local refinements (h-adaptivity) or enrichments (p-adaptivity) are applied in the spirit of the strategy proposed in [2]. The approximation error is reduced to a given level of accuracy with a minimal set of additional degrees of freedom. Numerical results on two 2D model problems illustrate both the validity of the error estimator presented and the efficiency of the adaptive procedure.