Numerical analysis for a variational/hemivariational type inequalities of Bingham fluids

This paper explores an analytical framework for an incompressible Bingham-type fluid (IBTF) within a bounded domain. The incompressible fluid model is expressed in its distributional form, which is formulated as a variational/hemivariational inequalities (VHF). Then, the well-posedness of a weak solution to the considered model is established. Ultimately, we employ the finite element approach to construct a discrete formulation of the framework and establish error bounds for the numerical approximations.