A Discrete Data Assimilation Algorithm for the Three Dimensional Planetary Geostrophic Equations of Large-Scale Ocean Circulation.

The main objective of this paper is to consider a discrete data assimilation algorithm for the three dimensional planetary geostrophic equations of large-scale ocean circulation in the case that the observable measurements, obtained discretely in time, may be contaminated by systematic errors, which works for a general class of observable measurements, such as low Fourier modes and local spatial averages over finite volume elements. We will provide some suitable conditions to establish asymptotic in time estimates of the difference between the approximating solution and the unknown exact (reference) solution in some appropriate norms for these two different kinds of interpolation operators, which also shows that the approximation solution of the proposed discrete data assimilation algorithm will convergent to the unique unknown exact (reference) solution of the original system at an exponential rate, asymptotically in time if the observational measurements are free of error. [ABSTRACT FROM AUTHOR]