The Formulation by Lions and Glowinski Sample Clauses

The Formulation by Lions and Glowinski. The mathematical and numerical problems associated with solving the Xxxxxxx fluid flow equations motivated researchers to consider different formulations of (1.2), (1.3). One approach is based on the variational inequality formulation introduced by Du- vaut and Lions [39]. A numerical solver based on this formulation was proposed by Glowinski et. al. (see [34] and the references therein) and is based on Uzawa-type it- erative schemes. It has become attractive when solving the non-regularized Xxxxxxx equations, especially when it is necessary to find the ‘true’ visco-plastic solution and to determine the plug regions [76, 80]. The idea of this approach is as follows: the solution u of the Xxxxxxx problem is equivalent to the minimization min v∈H1(Ω) J(v), with J(v) = µ ∫ Ω |Dv|2dx + τs ∫ Ω |Dv|dx − ∫ Ω