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Regularized finite element discretizations of a grade‐two fluid model

We consider a system with three unknowns in a two‐dimensional bounded domain which models the flow of a grade‐two non‐Newtonian fluid. We propose to compute an approximation of the solution of this problem in two steps: addition of a regularization term, finite element discretization of the regularized problem. We prove optimal a priori and a posteriori error estimates and present some numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.