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This paper presents a lowest-order immersed Raviart-Thomas mixed triangularfinite element method for solving elliptic interface problems on unfittedmeshes independent of the interface. In order to achieve the optimalconvergence rates on unfitted meshes, an immersed finite element finite (IFE)is constructed by modifying the traditional Raviart-Thomas element. Someimportant properties are derived including the unisolvence of IFE basisfunctions, the optimal approximation capabilities of the IFE space and thecorresponding commuting digram. Optimal error estimates are rigorously provedfor the mixed IFE method and some numerical examples are also provided tovalidate the theoretical analysis.

An immersed Raviart-Thomas mixed finite element method for elliptic interface problems on unfitted meshes