Speaker: Bikram Bir, IIT Bombay
Date and Time (of the first lecture): Thursday 16 March 2023 at 02.30PM
Venue: Ramanujan Hall, Department of Mathematics.
Title: Oldroyd Model of Order One: Theory and Numerics
Abstract: In these lectures, we discuss about a few finite element methods
for the equations of motion arising in the two-dimensional Oldroyd model
of order one; a model that represents linear viscoelastic fluid flows and
that can be viewed as an integral perturbation of the Navier-Stokes
equations.
First, we study existence and uniqueness of the continuous and weak
solution. Then, we discretize the space variable based on standard
Galerkin finite element method and the temporal variable based on
different time-discrete schemes. We next employ different finite element
methods like the two-grid method, the penalty method, the grad-div
stabilization method, the projection method and the nonconforming finite
element method. In all these cases, our main aim will be to obtain an
optimal error estimate for the velocity and the pressure. Finally, we
present some
numerical experiments to validate our theoretical findings.