Adjoint formalism and the configuration retrieval of an evolutionary system represented by Burgers' Equations,

P.S.D. Silva, I.M. Navon, L. Landau

4D variational data assimilation is proposed as an efficient procedure to determine a past configuration of a dynamical system of which only a few (and, under certain hypothesis, even partial) observations and its dynamics are known. The retrieved configuration is in good accordance with the test configuration. The leading mathematical concept, adjoint equations, and the role in the design of algorithms of the representation of the differential of a functional defined in a vectorial space with inner product are discussed in detail.

Keywords: Optimal control, adjoint equations, variational methods, data assimilation.