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

Picasso, M.Rappaz, J.2006-08-242006-08-242006-08-24200110.1051/m2an:2001140https://infoscience.epfl.ch/handle/20.500.14299/233717WOS:0001724998000031605In 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.viscoelastic fluidsGalerkin Least Square finite elementsFINITE-ELEMENT METHODSNUMERICAL-ANALYSISFLUID MODELAPPROXIMATIONEQUATIONSExistence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flowstext::journal::journal article::research article