Geodesic
Efficient three-level scheme for parabolic equations in cylindrical coordinates in a region with a small hole
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 445-456

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An efficient three-level scheme for parabolic equations in cylindrical coordinates is constructed in a region with a small hole. No axial symmetry is assumed. The convergence rate of the scheme is estimated under minimum requirements on the initial data. The estimates are uniform with respect to a small parameter – the inner diameter of the region. The order of convergence $\tau+h^2$, $\tau^{1/2}+h$, $\tau+h$, depending on the smoothness of the data. 
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     author = {E. I. Aksenova},
     title = {Efficient three-level scheme for parabolic equations in cylindrical coordinates in a~region with a~small hole},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {445--456},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a8/}
}
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E. I. Aksenova. Efficient three-level scheme for parabolic equations in cylindrical coordinates in a region with a small hole. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 445-456. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a8/