Speaker: Marc Laforest, Department of Mathematics, Colorado State University
Title: Error Estimation for Lagrangian Methods
 
Abstract:
Lagrangian methods for the numerical computation of fluid
flow are inexpensive finite element methods based on the
flow equations in Lagrangian coordinates. Points
in the mesh can therefore be identified with particles in
the flow and the mesh may become distorted as the flow evolves.
For engineering applications, it is useful to have an inexpensive
yet reliable error metric that can be implemented in a
transparent manner into existing codes.
 
In this talk, we present joint work with Tom Voth
on two error indicators for Lagrangian
methods. The first is based on a weak formulation of the residual.
This is a convenient way of computing the residual for
approximations constructed from discontinuous elements
for the density and the pressure. This approach is based 
on earlier work by Karni and Kurganov.
A second error estimator is constructed by enriching the
test and trial spaces by bubble elements and measuring the
error components in these extensions. 
Under some assumptions the equations can be localized
and indication of the spatial error. Numerical 
examples will also be presented.