Geodesic
On using the Lagrange coefficients for a~posteriori error estimation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 4, pp. 375-388.

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A posteriori error estimation of the goal functional is considered using a differential presentation of a finite difference scheme and adjoint equations. The local approximation error is presented as a Tailor series remainder in the Lagrange form. The field of the Lagrange coefficients is determined by a high accuracy finite difference stencil affecting results of computation. The feasibility of using the Lagrange coefficients for the refining solution and estimation of its uncertainty are considered. 
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A. K. Alekseev; I. N. Makhnev. On using the Lagrange coefficients for a~posteriori error estimation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 4, pp. 375-388. http://geodesic.mathdoc.fr/item/SJVM_2009_12_4_a1/

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