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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2022_519_a8,
     author = {S. Repin},
     title = {A posteriori error identities for parabolic convection--diffusion problems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {205--228},
     publisher = {mathdoc},
     volume = {519},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a8/}
}
TY  - JOUR
AU  - S. Repin
TI  - A posteriori error identities for parabolic convection--diffusion problems
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 205
EP  - 228
VL  - 519
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a8/
LA  - en
ID  - ZNSL_2022_519_a8
ER  - 
%0 Journal Article
%A S. Repin
%T A posteriori error identities for parabolic convection--diffusion problems
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 205-228
%V 519
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_519_a8/
%G en
%F ZNSL_2022_519_a8
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/