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In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain.
Mathematical and numerical aspects of viscoelastic flows are investigated here. Two simplified mathematical models are considered. They are motivated by a splitting algorithm for solving viscoelastic
A reflected diffusion process is proposed for modeling of viscoelastic fluids. In order to define the viscoelastic stress tensor, the reflected diffusion process is approximated by Ito diffusions with