**A Variational Solution to the Transport Equation
Subject to an Affine Constraint
**

** Philipp~P. Pébay (Sandia National Laboratories, MS 9051 PO Box 969,
Livermore CA 94550, U.S.A.)
**

*Abstract.*
During this presentation, we establish an existence and uniqueness
theorem for the transport equation subject to an inequality affine
constraint, viewed as a constrained optimization problem. Then we
derive a Space-Time Integrated Least Squares (STILS) scheme for its
numerical approximation. Furthermore, we discuss some
L^2-projection strategies and with numerical examples we
show that there are not relevant for that problem.

Work in collaboration with J. Pousin (INSA Lyon),
H. Najm (Sandia) and M. Picq (INSA Lyon). The author
is supported by the United States Department of Energy, Office of
Defense Programs.

*Reference.*
J. G. Pousin, P. P. Pébay, M. Picq and H. N. Najm,
A variational solution to the transport equation subject to an
affine constraint,
Sandia Technical Report, SAND2004-8096,
Sandia National Laboratories, February 2004.