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We propose a semismooth Newton method for non-Newtonian models ofincompressible flow where the constitutive relation between the shear stressand the symmetric velocity gradient is given implicitly; this class ofconstitutive relations captures for instance the models of Bingham andHerschel-Bulkley. The proposed method avoids the use of variationalinequalities and is based on a particularly simple regularisation for which the(weak) convergence of the approximate stresses is known to hold. The system isanalysed at the function space level and results in mesh-independent behaviourof the nonlinear iterations.

A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow