New immersed finite volume element method for elliptic interface problems with non-homogeneous jump conditions

In this paper, we propose a new immersed finite volume element method to solve elliptic problems with discontinuous diffusion coefficient and sharp-edged interfaces on Cartesian mesh. The method uses the non-traditional immersed finite volume element method together with additional immersed finite element function on interface element. It can deal with the case when the solution or its normal derivative is discontinuous. Extensive numerical experiments for various problems show that the new method is approximate second-order convergence in the L∞ norm for piecewise smooth solutions, and more than 1.65th order accuracy is observed for solution with singularity. •The proposed IFVE method is second-order accuracy in the L∞ norm for the elliptic interface problems for all examples tested.•The new method can deal with the case when the solution or its normal derivative is discontinuous.•The new method can handle the case where the interface has sharp edge or meets with the vertices.