Geodesic
Application of SDE's to estimating the solution of heat equations with discontinuous coefficients
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 147-161

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This paper proposes the use of the numerical solution to stochastic differential equations (SDE's) to find estimates of the solutions to boundary value problems for linear parabolic equations with discontinuous coefficients. The solution of the problem with smoothed coefficients is taken as an approximation of the generalized solution to the considered boundary value problem. The results of calculations for a thermal barrier coating comprising a composite cellular material are presented. 
@article{SJVM_2015_18_2_a3,
     author = {S. A. Gusev},
     title = {Application of {SDE's} to estimating the solution of heat equations with discontinuous coefficients},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {147--161},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a3/}
}
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S. A. Gusev. Application of SDE's to estimating the solution of heat equations with discontinuous coefficients. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 147-161. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a3/