Geodesic
On the error transfer calculation via adjoint equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 325-334.

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The calculation of a flow parameter uncertainty depending on the error in input data: initial conditions, boundary conditions, coefficients may be conducted using adjoint equations. For the pointwise error estimation, this approach is advantageous from the computational standpoint since it needs solving only one (adjoint) system of equations in addition to the system that simulates a flowfield. The fields of “adjoint temperature”, “adjoint density”, etc. enable the calculation of an impact of any input data error on the uncertainty of a reference pointwise parameter. The considered approach can be applied to the estimation of a functional variation under the action of a small random error or a variation of input data away from a stationary point. In the vicinity of such a stationary point, the error can also be computed using adjoint equations but with much higher computational costs. 
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A. K. Alekseev. On the error transfer calculation via adjoint equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 4, pp. 325-334. http://geodesic.mathdoc.fr/item/SJVM_2007_10_4_a0/

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