Geodesic
Vector domain decomposition schemes for parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1530-1547

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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. 
@article{ZVMMF_2017_57_9_a9,
     author = {P. N. Vabishchevich},
     title = {Vector domain decomposition schemes for parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1530--1547},
     publisher = {mathdoc},
     volume = {57},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a9/}
}
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P. N. Vabishchevich. Vector domain decomposition schemes for parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 9, pp. 1530-1547. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_9_a9/