| Abstract: | 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 FVE 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(h2) (in L2 norm)
and O(h) (in H1 norm) convergence rates. |
