An immersed finite element method for anisotropic flow models in porous medium

In this paper we develop an immersed interface finite element method for a kind of anisotropy diffusion models governed by the elliptic interface problems with discontinuous tensor-coefficients. The method is based on linear polynomials on non-interface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H
¹
- norm and L
²
-norm.