A Two-level Finite Element Method for Viscoelastic Fluid Flow: Non-smooth Initial Data

Abstract

In this article, we analyze a two-level finite element method for the equations of motion arising in the flow of 2D Oldroyd model with non-smooth initial data. It involves solving the non-linear problem on a coarse grid of mesh-size $H$ and solving a linearized problem on a fine grid of mesh-size $h,h<<H$. The method gives optimal convergence rate for velocity in $H^1$-norm and for pressure in $L^2$-norm. The analysis takes in to account the loss of regularity of the solution of the Oldroyd model at initial time.

arXiv admin note: substantial text overlap with arXiv:1211.3342

References in corpus (2)

• Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
• Backward Euler method for the Equations of Motion Arising in Oldroyd Fluids of Order One with Nonsmooth Initial Data