Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions.

In this paper, a new bilinear immersed finite volume element method based on rectangular mesh is presented to solve the elliptic interface problems with non-homogeneous jump conditions and sharp-edged interfaces. This method is capable of dealing with the case when the interface passes through grid points and when the solutions are oscillating. Plenty of numerical experiments show that our method is nearly second-order accuracy for the solution and is first-order accuracy for the gradient of the solution in the L ∞ norm. • The proposed bilinear IFVE method can deal with the case when the solution or its normal derivative is discontinuous. • Numerical results demonstrate that the method is second-order accuracy for the solution in the L ∞ norm. • The new method can solve the crack problem provided that the mesh is fine enough. [ABSTRACT FROM AUTHOR]