Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces

摘要

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.