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 thebilinear immersed finite element (IFE) for solving the boundary value problems of thediffusion equation with a discontinuous coefficient (interface problem). This methodpossesses the usual FVE method\u27s local conservation property and can use a structuredmesh or even the Cartesian mesh to solve a boundary value problem whose coefficienthas discontinuity along piecewise smooth nontrivial curves. Numerical examples areprovided to demonstrate features of this method. In particular, this method can pro-duce a numerical solution to an interface problem with the usualO(h2) (in L2 norm) an dO(h) (in H1 norm) convergence rates