Publication

Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

Jacques Rappaz, Marco Picasso
2001
Journal Articles

Abstract

In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived. An Elastic Viscous Split Stress (EVSS) scheme related to the GLS method is introduced. Numerical results confirm the theoretical predictions.

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https://infoscience.epfl.ch/entities/publication/dd657f8b-8c04-4988-832c-479d62d50d3b

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Jacques Rappaz, Marco Picasso
2001
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/dd657f8b-8c04-4988-832c-479d62d50d3b

About this result

Related concepts (32)

Viscoelasticity

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.

Generalized least squares

In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in the regression model. Least squares and weighted least squares may need to be more statistically efficient and prevent misleading inferences. GLS was first described by Alexander Aitken in 1935. In standard linear regression models one observes data on n statistical units.

Reduced chi-squared statistic

In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) It is defined as chi-square per degree of freedom: where the chi-squared is a weighted sum of squared deviations: with inputs: variance , observations O, and calculated data C.

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Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

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