A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient (Communications in Computational Physics, 2009)
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's 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 producea numerical solution to an interface problem with the usual O(h2) (in L2 norm)and O(h) (in H1 norm) convergence rates.
Keywords: Interface problems; immersed interface; finite volume element; discontinuous coefficient; diffusion equation.