Fang, F.; Pain, C. C.; Piggott, M. D.; Gorman, G. J.; Goddard, A. J. H. An adaptive mesh adjoint data assimilation method applied to free surface flows. (English) Zbl 1134.86004 Int. J. Numer. Methods Fluids 47, No. 8-9, 995-1001 (2005). Summary: We describe the construction of a three-dimensional adaptive mesh data assimilation method for oceanographic/coastal applications, including a free surface. This is the first attempt at introducing a moving computational domain into an adjoint model with mesh adaptivity. We also provide insight into the feasibility and reliability of the adaptive mesh adjoint model. The use of differing adapting meshes for forward and adjoint problems is considered here, where each mesh is optimized with respect to the individual properties of each solution. The free surface test case considered is that of flow in a two-dimensional vertical fluid slice. In this test case the sea surface elevation boundary conditions is optimized by assimilating sea surface height observations. The feasibility of an assimilation approach on adapting moving domains is demonstrated by comparison with a fixed mesh result. Cited in 3 Documents MSC: 86-08 Computational methods for problems pertaining to geophysics 86A05 Hydrology, hydrography, oceanography Keywords:data assimilation; free surface; adjoint; finite element; unstructured adaptive mesh Software:TAF; L-BFGS; TAMC PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 47, No. 8--9, 995--1001 (2005; Zbl 1134.86004) Full Text: DOI References: [1] . Inverse Methods in Physical Oceanography. Cambridge University Press: Cambridge, 1992. · Zbl 0782.76002 [2] Tziperman, Journal of Physical Oceanography 22 pp 1458– (1992) [3] Talagrand, Quarterly Journal of the Royal Meteorological Society 113 pp 1311– (1987) [4] . Perspectives in Flow Control and Optimization. SIAM: Philadelphia, 2003. [5] Farrell, Journal of Physical Oceanography 22 pp 338– (1992) [6] Wenzel, Progress in Oceanography 48 pp 73– (2001) [7] Daescu, Meteorology and Atmospheric Physics 85 pp 205– (2004) [8] Courtier, Quarterly Journal of the Royal Meteorological Society 120 pp 1367– (1994) [9] Bosseur, Computers and Mathematics with Applications 43 pp 1559– (2002) [10] Annan, Estuarine, Coastal and Shelf Science 53 pp 459– (2001) [11] Ford, Monthly Weather Review 132 pp 2816– (2004) [12] Pain, Computer Methods in Applied Mechanics and Engineering 190 pp 3771– (2001) [13] , , , , , , , . Adjoint data assimilation into a 3D unstructured mesh coastal finite element model. In Proceedings of the 8th International Conference on Estuarine and Coastal Modeling, Monterey, CA, 3-5 November 2003, Spaulding ML (ed.), ASCE, 2004; 308-324. [14] Piggott, Ocean Modelling (2004) [15] . Neural Networks for Pattern Recognition. Oxford University Press: Oxford, 1995. [16] , . Incompressible Flow and the Finite Element Method. Wiley: New York, 1998. [17] Hughes, Computer Methods in Applied Mechanics and Engineering 58 pp 329– (1986) [18] Pain, Ocean Modelling (2004) [19] Alekseev, International Journal of Computational Fluid Dynamics 16 pp 113– (2002) [20] Moore, Journal of Physical Oceanography 21 pp 398– (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.