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In this paper, a nonlinear problem corresponding to a simplied 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 nite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and ap riorierror estimates are established using a Newton-chord xed 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 conrm the theoretical predictions.

modélisation mathématique et analyse numérique

Existence,a priorianda posteriorierror estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows