Geodesic
A posteriori error identities for parabolic convection–diffusion problems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 50, Tome 519 (2022), pp. 205-228 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, we derive and discuss integral identities that hold for the difference between the exact solution of initial-boundary value problems generated by the reaction–convection–diffusion equation and any arbitrary function from admissible (energy) class. One side of the identity forms a natural measure of the distance between the exact solution and its approximation, while the other one is either directly computable or natural measure serves as a source of fully computable error bounds. A posteriori error identities and error estimates are derived in the most general form without using special features of a function compared with the exact solution. Therefore, they are valid for a wide spectrum of approximations constructed different numerical methods and can be also used for the evaluation of modelling errors. 
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S. Repin. A posteriori error identities for parabolic convection–diffusion problems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 50, Tome 519 (2022), pp. 205-228. http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a8/

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