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

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