Geodesic
The rates of convergence of the finite difference schemes on nonuniform meshes for parabolic equation with variable coefficients and weak solutions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 123-136

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The convergence of the difference schemes of the second order of local approximation on space for a onedimensional heat conduction equation with variable factors on an arbitrary nonuniform grid is investigated. For the schemes with averaged coefficient of a thermal conduction and averaged right part the evaluations of a rate of convergence in a grid norm $L_2$, agreed with a smoothness of a solution of a boundary value problem are obtained. 
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     author = {B. S. Jovanovi\'c and P. P. Matus and V. S. Shchehlik},
     title = {The rates of convergence of the finite difference schemes on nonuniform meshes for parabolic equation with variable coefficients and weak solutions},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {123--136},
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     volume = {2},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a2/}
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B. S. Jovanović; P. P. Matus; V. S. Shchehlik. The rates of convergence of the finite difference schemes on nonuniform meshes for parabolic equation with variable coefficients and weak solutions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 2, pp. 123-136. http://geodesic.mathdoc.fr/item/SJVM_1999_2_2_a2/