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

TL;DR

This paper presents a two-level finite element method for 2D Oldroyd model fluid flow with non-smooth initial data, achieving optimal convergence rates while accounting for initial regularity loss.

Contribution

It introduces a novel two-level finite element approach that efficiently handles non-smooth initial data in viscoelastic fluid flow simulations.

Findings

Optimal convergence for velocity in H^1-norm.

Optimal convergence for pressure in L^2-norm.

Method effectively manages initial regularity loss.

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.