Geodesic
Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1

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This article presents second-order difference schemes of 2-D and 3-D elliptic problems with intersecting interfaces. The discretization is made using new Marchuk identities. It possesses the typical for the method advantages as conservatism, second-order accuracy even at low smoothness of the differential problem solution. The convergence and accuracy are discussed theoretically and experimentally. Numerical tests show the feasiblity of the schemes. 
@article{KJM_2007_30_1_a20,
     author = {Ivanka Tr. Angelova and Lubin G. Vulkov},
     title = {Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces},
     journal = {Kragujevac Journal of Mathematics},
     pages = {277 - 292},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2007},
     zbl = {1199.65358},
     url = {http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a20/}
}
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Ivanka Tr. Angelova; Lubin G. Vulkov. Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces. Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1. http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a20/