A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient

This paper is to present a finite volume element (FVE) method based on the bilinear immersed finite element (IFE) for solving the boundary value problems of the diffusion equation with a discontinuous coefficient (interface problem). This method possesses the usual WE method's local conservation property and can use a structured mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient has discontinuity along piecewise smooth nontrivial curves. Numerical examples are provided to demonstrate features of this method. In particular, this method can produce a numerical solution to an interface problem with the usual O(h(2)) (in L-2 norm) and O(h) (in H-1 norm) convergence rates.