Geodesic
An estimation of point-wise approximation error using
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 343-358

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

The present paper is addressed to the estimation of the local (point-wise) approximation error on the ensemble of the numerical solutions obtained using independent algorithms. The variational inverse problem is posed for the approximation error estimation. The considered problem is ill-posed due to invariance of the governing equations to the shift transformations. By this reason, the zero order Tikhonov regularization is applied. The numerical tests for the two-dimensional equations describing the inviscid compressible flow are performed in order to verify the efficiency of considered algorithm. The estimates of approximation errors, obtained by the considered inverse problem, demonstrate the satisfactory accordance with the Richardson extrapolation results at significantly less computational costs. 
@article{SJVM_2022_25_4_a0,
     author = {A. K. Alekseev and A. E. Bondarev},
     title = {An estimation of point-wise approximation error using},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {343--358},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a0/}
}
TY  - JOUR
AU  - A. K. Alekseev
AU  - A. E. Bondarev
TI  - An estimation of point-wise approximation error using
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2022
SP  - 343
EP  - 358
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a0/
LA  - ru
ID  - SJVM_2022_25_4_a0
ER  - 
%0 Journal Article
%A A. K. Alekseev
%A A. E. Bondarev
%T An estimation of point-wise approximation error using
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2022
%P 343-358
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a0/
%G ru
%F SJVM_2022_25_4_a0
A. K. Alekseev; A. E. Bondarev. An estimation of point-wise approximation error using. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 343-358. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a0/