Geodesic
The flux predictor-corrector scheme for solving a~3D heat transfer problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 345-358.

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

In this paper we propose and study the flux predictor-corrector scheme in the three-dimensional case. This scheme is depleted of drawbacks of that constructed on the basis of the Douglas–Gunn prototype-scheme. The scheme proposed demonstrates the second order of accuracy. 
@article{SJVM_2017_20_4_a0,
     author = {K. V. Voronin and Yu. M. Laevsky},
     title = {The flux predictor-corrector scheme for solving {a~3D} heat transfer problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {345--358},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a0/}
}
TY  - JOUR
AU  - K. V. Voronin
AU  - Yu. M. Laevsky
TI  - The flux predictor-corrector scheme for solving a~3D heat transfer problem
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2017
SP  - 345
EP  - 358
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a0/
LA  - ru
ID  - SJVM_2017_20_4_a0
ER  - 
%0 Journal Article
%A K. V. Voronin
%A Yu. M. Laevsky
%T The flux predictor-corrector scheme for solving a~3D heat transfer problem
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2017
%P 345-358
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a0/
%G ru
%F SJVM_2017_20_4_a0
K. V. Voronin; Yu. M. Laevsky. The flux predictor-corrector scheme for solving a~3D heat transfer problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 345-358. http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a0/

[1] Voronin K. V., Laevsky Yu. M., “On splitting schemes in the mixed finite element method”, Numerical Analysis and Applications, 5:2 (2012), 150–155 | DOI | Zbl

[2] Voronin K. V., Laevsky Yu. M., “Splitting schemes in the mixed finite-element method for the solution of heat transfer problems”, Mathematical Models and Computer Simulations, 5:2 (2013), 167–174 | DOI | MR | Zbl

[3] Voronin K. V., Laevskii Yu. M., “Ob odnom podkhode k postroeniyu potokovykh skhem rasschepleniya v smeshannom metode konechnykh elementov”, Matematicheskoe modelirovanie, 26:12 (2014), 33–47 | Zbl

[4] Voronin K. V., Laevsky Yu. M., “On the stability of some flux splitting schemes”, Numerical Analysis and Applications, 8:2 (2015), 113–121 | DOI | DOI | MR | Zbl

[5] Voronin K. V., Laevsky Yu. M., “A new approach to constructing splitting schemes in mixed FEM for heat transfer: a priori estimates”, Lecture Notes in Computer Science, 9045, 2015, 417–425 | DOI | MR | Zbl

[6] Voronin K. V., Laevsky Yu. M., “On splitting schemes of predictor-corrector type in mixed finite element method”, Siberian Electronic Mathematical Reports, 12 (2015), 752–765 | DOI | MR | Zbl

[7] Voronin K. V., Laevsky Yu. M., “A new approach to constructing vector splitting schemes in mixed finite element method for parabolic problems”, J. of Numerical Mathematics, 25:1 (2017), 17–34 | DOI | MR | Zbl

[8] Raviart P.-A., Thomas J. M., “A mixed finite element method for 2-nd order elliptic problems”, Lecture Notes in Mathematics, 606, 1977, 292–315 | DOI | MR | Zbl

[9] Peaceman D. W., Rachford H. H. (Jr.), “The numerical solution of parabolic and elliptic differential equations”, J. Soc. Indust. Appl. Math., 3:1 (1955), 28–41 | DOI | MR | Zbl

[10] Douglas J. (Jr.), Gunn J. E., “A general formulation of alternating direction methods”, Numerische Mathematik, 6:1 (1964), 428–453 | DOI | MR | Zbl

[11] Samarskii A. A., “Lokalno-odnomernye raznostnye skhemy na neravnomernykh setkakh”, Zhurn. vychisl. matem. i mat. fiziki, 3:3 (1963), 431–466 | MR | Zbl

[12] Yanenko N. N., The Method of Fractional Steps, Springer-Verlag, New York, 1971 | Zbl

[13] Douglas J. (Jr.), “Alternating direction methods for three space variables”, Numerische Mathematik, 4:1 (1962), 41–63 | DOI | MR | Zbl

[14] Arbogast T., Huang C.-S., Yang S.-M., “Improved accuracy for alternating-direction methods for parabolic equations based on regular and mixed finite elements”, Mathematical Models and Methods in Applied Sciences, 17:8 (2007), 1279–1305 | DOI | MR | Zbl

[15] Brezzi P., Fortin M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991 | MR | Zbl

[16] Vabishchevich P. N., “Flux-splitting schemes for parabolic problems”, Computational Mathematics and Mathematical Physics, 52:8 (2012), 1128–1138 | DOI | MR

[17] Vabishchevich P. N., Additive Operator-Difference Schemes, de Gruyter, Berlin, 2013 | MR

[18] Marchuk G. I., Splitting Methods, Nauka, Moscow, 1988 | MR

[19] Richtmyer G. I., Morton K. W., Difference Methods for Initial-Value Problems, Jhon Wiley and Sons, New York, 1967 | MR