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On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model

Aseel Farhat, Evelyn Lunasin, Edriss S. Titi (2016)

Mathematics of Climate and Weather Forecasting

Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...

Optimal control and numerical adaptivity for advection–diffusion equations

Luca Dede', Alfio Quarteroni (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...

Optimal control and numerical adaptivity for advection–diffusion equations

Luca Dede', Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from...

Optimal Convective Heat-Transport

Josef Dalík, Oto Přibyl (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The one-dimensional steady-state convection-diffusion problem for the unknown temperature y ( x ) of a medium entering the interval ( a , b ) with the temperature y min and flowing with a positive velocity v ( x ) is studied. The medium is being heated with an intensity corresponding to y max - y ( x ) for a constant y max > y min . We are looking for a velocity v ( x ) with a given average such that the outflow temperature y ( b ) is maximal and discuss the influence of the boundary condition at the point b on the “maximizing” function v ( x ) .

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