Geodesic
A posteriori error estimation of a finite difference solution based on adjoint equations and differential representations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1213-1225

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Numerical results obtained for the parabolized Navier–Stokes equations are used to show that the error in computed flow parameters caused by the truncation error of the underlying finite difference scheme can be evaluated using adjoint equations. If the local truncation error is determined in terms of the Lagrange remainder of a Taylor series, the numerical results can be improved and the remaining error can be estimated from above. 
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     author = {A. K. Alekseev},
     title = {A posteriori error estimation of a finite difference solution based on adjoint equations and differential representations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1213--1225},
     publisher = {mathdoc},
     volume = {45},
     number = {7},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a7/}
}
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A. K. Alekseev. A posteriori error estimation of a finite difference solution based on adjoint equations and differential representations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1213-1225. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a7/