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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 9, Pages 1530–1547 (Mi zvmmf10616)  

Vector domain decomposition schemes for parabolic equations

P. N. Vabishchevichab

a Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia
b Ammosov North-Eastern Federal University, Yakutsk, Russia

Abstract: A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.

Key words: evolution equation, parabolic equation, finite element method, domain decomposition method, difference scheme, stability of difference schemes.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00785_а


DOI: https://doi.org/10.7868/S0044466917090137

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:9, 1511–1527

Bibliographic databases:

UDC: 519.63
Received: 20.10.2016

Citation: P. N. Vabishchevich, “Vector domain decomposition schemes for parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:9 (2017), 1530–1547; Comput. Math. Math. Phys., 57:9 (2017), 1511–1527

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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