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Almost all materials are anisotropic. In this paper, interface relations ofanisotropic elliptic partial differential equations involving discontinuitiesacross interfaces are derived in two and three dimensions. Compared withisotropic cases, the invariance of partial differential equations and the jumpconditions under orthogonal coordinates transformation is not valid anymore. Asystematic approach to derive the interface relations is established in thispaper for anisotropic elliptic interface problems, which can be important forderiving high order accurate numerical methods.

On jump relations of anisotropic elliptic interface problems