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

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

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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.

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