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By choosing the trial function space to the immersed finite element space and the test function space to be piecewise constant function space, we develop a discontinuous Galerkin immersed finite volume element method to solve numerically a kind of anisotropic diffusion models governed by the elliptic interface problems with discontinuous tensor-conductivity. The existence and uniqueness of the discrete scheme are proved, and an optimal-order energy-norm estimate and L2-norm estimate for the numerical solution are derived

Discontinuous Galerkin Immersed Finite Volume Element Method for Anisotropic Flow Models in Porous Medium