Geodesic
Implicit scheme on different time meshes for semilinear parabolic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 151-158.

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A method of the construction of difference schemes with different time-step in the subdomains is suggested. It is associated with the interpolation of a solution on a boundary of subdomains. In the case of a semilinear parabolic equation, it is proved that the solution of difference problem converges to that of a differential problem with the order $O(\tau)$. 
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V. I. Drobyshevich. Implicit scheme on different time meshes for semilinear parabolic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 2, pp. 151-158. http://geodesic.mathdoc.fr/item/SJVM_2000_3_2_a5/

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